ROUNDING OFF NUMBERS

To be able to round off numbers, you have to study the place value chart and use that knowledge to identify the value of each of the digits in the number.

The place value chart starts from ones to tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions and billions.

When given a number you start placing the values of each digit from the right digit to the left.

For example, the number 5,234,123,502 can be placed in the place order chart as below:

Billions	Hundred Millions	Ten Millions	Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
9	2	3	4	1	6	8	5	0	7

Once you know the place of a digit, you can add 0s to the remaining part at the right to know its place value

For instance the place of the digit,9 is billions and its place value is 9,000,000,000.

The place of the digit, 2 is hundred millions and its place value is 200,000,000

The place of the digit, 3 is ten millions and its place value is 30,000,000

The place of the digit, 4 is millions and its place value is 4,000,000

The place of the digit, 1 is hundred thousands and its place value is 100,000

The place of the digit, 6 is ten thousands and its place value is 60,000

The place of the digit, 8 is thousands and its place value is 8,000

The place of the digit, 5 is hundreds and its place value is 500

The place of the digit, 0 is tens and its place values is 00

The place of the digit, 7 is ones and its place value is 7

Rounding to the nearest place value

Step 1: Locate the digit in front of the place you are to round the number to. Thus if hundred thousand, locate the digit in the ten thousand, if ten thousand, locate the digit in thousands, etc.

Step 2: If the digit in front is 5 or more, add 1 to the digit of the place you are rounding to but if not maintain the digit.

Step 3: Replace the digit in front of the place you are to round the number to by zeros (0s)

Examples

1. Round 9,234,168,507 to the nearest hundred thousand.

Step 1

Locate the digit in front of the place you are to round the number to. Thus if hundred thousand, locate the digit in the ten thousand, if ten thousand, locate the digit in thousands, if thousand, locate the digit in the hundred,etc.

We are to round to the nearest hundred thousand.

The digit in front of the hundred thousand place is 6

Step 2

If the digit in front is 5 or more, add 1 to the digit of the place you are rounding to but if not maintain the digit.

The digit of the place we are rounding to is 1 (the hundred thousand place). Since the digit in front of it is 6 and more than 5, we have to add 1 to the digit at the hundred thousand place (1) making 1+1 = 2

Step 3

Replace the digit in front of the place you are to round the number to by zeros (0s)

6,8,5,0 and 7 which are in front of the hundred thousand place is replaced by 0s

9,234,168,507 to the nearest hundred thousand = 9,234,200,000

2. Round 4,812,539,764 to the nearest hundred thousand.

Step 1

Locate the digit in front of the place you are to round the number to. Thus if hundred thousand, locate the digit in the ten thousand, if ten thousand, locate the digit in thousands, if thousand, locate the digit in the hundred,etc.

We are to round to the nearest hundred thousand.

The digit in front of the hundred thousand place is 3

Step 2

If the digit in front is 5 or more, add 1 to the digit of the place you are rounding to but if not maintain the digit.

The digit of the place we are rounding to is 5 (the hundred thousand place). Since the digit in front of it is 3 and less than 5, we maintain the digit 5

Step 3

Replace the digit in front of the place you are to round the number to by zeros (0s)

3,9,7,6 and 4 which are in front of the hundred thousand place is replaced by 0s

4,812,539,764 to the nearest hundred thousand = 4,812,500,000

3. Round 3281 to the nearest hundred.

Step 1

Locate the digit in front of the place you are to round the number to. Thus if hundred thousand, locate the digit in the ten thousand, if ten thousand, locate the digit in thousands, if thousand, locate the digit in the hundred,etc.

We are to round to the nearest hundred.

The digit in front of the hundred place is 8

Step 2

If the digit in front is 5 or more, add 1 to the digit of the place you are rounding to but if not maintain the digit.

The digit of the place we are rounding to is 2 (the hundred place). Since the digit in front of it is 8 and more than 5, we add 1 to 2 making 1+2 = 3.

Step 3

Replace the digit in front of the place you are to round the number to by zeros (0s)

8 and 1 which are in front of the hundred place is replaced by 0s

3281 to the nearest hundred = 3,300

4. Round 4216 to the nearest hundred

Step 1

Locate the digit in front of the place you are to round the number to. Thus if hundred thousand, locate the digit in the ten thousand, if ten thousand, locate the digit in thousands, if thousand, locate the digit in the hundred,etc.

We are to round to the nearest hundred.

The digit in front of the hundred place is 1

Step 2

If the digit in front is 5 or more, add 1 to the digit of the place you are rounding to but if not maintain the digit.

The digit of the place we are rounding to is 2 (the hundred place). Since the digit in front of it is 1 and less than 5, we maintain the digit at the hundred place (2)

Step 3

Replace the digit in front of the place you are to round the number to by zeros (0s)

1 and 6 which are in front of the hundred place is replaced by 0s

4216 to the nearest hundred = 4,200

5. Round 4559 to the nearest thousand.

Step 1

Locate the digit in front of the place you are to round the number to. Thus if hundred thousand, locate the digit in the ten thousand, if ten thousand, locate the digit in thousands, if thousand, locate the digit in the hundred,etc.

We are to round to the nearest thousand.

The digit in front of the thousand place is 5

Step 2

If the digit in front is 5 or more, add 1 to the digit of the place you are rounding to but if not maintain the digit.

The digit of the place we are rounding to is 4 (the thousand place). Since the digit in front of it is 5, we add 1 to 4 making 1+4 = 5.

Step 3

Replace the digit in front of the place you are to round the number to by zeros (0s)

5,5 and 9 which are in front of the thousand place is replaced by 0s

4559 to the nearest thousand = 5,000

6. Round 4295 to the nearest thousand.

Step 1

Locate the digit in front of the place you are to round the number to. Thus if hundred thousand, locate the digit in the ten thousand, if ten thousand, locate the digit in thousands, if thousand, locate the digit in the hundred,etc.

We are to round to the nearest thousand.

The digit in front of the thousand place is 2

Step 2

If the digit in front is 5 or more, add 1 to the digit of the place you are rounding to but if not maintain the digit.

The digit of the place we are rounding to is 4 (the thousand place). Since the digit in front of it is 2 and not 5 or more, we maintain the digit in the thousand place.

Step 3

Replace the digit in front of the place you are to round the number to by zeros (0s)

2,9 and 5 which are in front of the thousand place is replaced by 0s

4559 to the nearest thousand = 4,000

APPLICATION OF KNOWLEDGE

Question 1

Write ₵35,632.00 correct to the nearest thousand cedis.

A. ₵40,000.00 B. ₵36,000.00 C. ₵35,000.00 D. ₵35,000.00

[B.E.C.E 1994 Section A Question 25]

Solution

Question 2

Write 78910 correct to the nearest thousand.

A. 70,000 B. 78,000 C. 79,000 D. 80,000

[B.E.C.E 2004 Section A Question 8]

Solution

Question 3

What is the value of 4 in the number 2 043 507?

A. forty B. four hundred C. four-thousand D. fourty-thousand

[B.E.C.E 2004 Section A Question 8]

Solution

Question 4

Round 8921465 to the nearest hundred.

A. 892100 B. 8921400 C. 8921460 D. 8921500

[B.E.C.E 2008 Section A Question 3]

Solution

Question 5

Correct 48,947.2547 to the nearest hundred.

A. 490 B. 48,900 C. 48,950 D. 49,000

[B.E.C.E 2016 Section A Question 6]

NOTE: The decimal part(the digits after the point, .) is excluded

Solution

Significant figures

Significant figures (or significant digits) are the number of digits important to determine the accuracy and precision of measurement, such as length, mass, or volume.

Significant digits in math convey the value of a number with accuracy. They are considered substantial figures that contribute to the precision of a number.

Rules to determine the number of significant figures in a number

1. Leading zeros are not significant
2. Non-zeros are significant
3. Zeros in between non-zero digits are significant
4. Trailing zeros to the right of the decimal point are significant

Examples

How to Round Off Significant Figures

To round off significant figures, we have to omit one or more digits from the right side of the number until we reach the number of significant digits that we want to round it off to.

First, we have to look at the digit on the right end of the number (to the right of the digit we want to round it off to).

If the digit is lower than 5, the number is rounded off to the lower number.

If the digit is greater than or equal to 5, the number is rounded up to the higher number.

If the number to be rounded off is a whole number, the remaining significant figures are replaced by 0.

Examples

1. Round 0.04582 to three significant figures

The significant figures are 4,5,8,2

The three significant figure lands on 8.

Check if the next significant figure is 5 or more, if it is add 1 to the digit of where the significant figure is round to.

The next significant figure after 8 is 2, hence there is no need to add 1

0.04582 to three significant figures is 0.458

2. Round 12.378162 to four significant figures

The significant figures are 1,2,3,7,8,1,6 and 2

The fourth significant figure is 7

The next significant figure after the fourth is 8 which is more than 5, hence we add 1 to the fourth significant figure making 7+1 = 8

12.378162 to four significant figure is 12.38

3. Round 42,768 to two significant figures.

The significant figures are 4,2,7,6 and 8

The second significant figure is 2

The significant figure next to that is 7 which is more than 5, hence we add 1 to the second significant figure making 2+1 = 3.

Since its a whole number, the rest of the digits are replaced by 0, thus 7,6 and 3 are replaced by 0s

42,768 two significant figures is 43,000

APPLICATION OF KNOWLEDGE

Question 6

Write 39.9748 km, correct to three significant figures.

A. 39.9 km B. 39.975 km C. 40 km D. 40.0 km

[B.E.C.E 1993 Section A Question 30]

Solution

Question 7

Correct 0.00025 to one significant figure.

A. 0.2 B. 0.003 C. 0.0002 D. 0.0003

[B.E.C.E 2002B Section A Question 12]

Solution

Question 8

Correct 0.003858 to three significant figures.

A. 0.00385 B. 0.00386 C. 0.0039 D. 386

[B.E.C.E 2006 Section A Question 8]

Solution

Rounding off of decimal numbers

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

Example 1.5 is a decimal number. The part before the point (.) is the whole number part and the one after the point is the fraction part. In 1.5, the 1 is the whole part and the 0.5 is the fraction part.

Place value of digits in decimal number

The first place after the decimal point is called the "tenths", which represents a place value of $\frac{1}{10}$ of the whole or one-tenth of the whole. In decimal form, this fraction is written as "0.1".

Such fractions whose denominator is 10 or a positive power of 10 is called a decimal fraction.

The second place is called the "hundredths", which represents a place value of $\frac{1}{100}$ of the whole or one-hundredth of the whole. In numerical form, this decimal fraction is written as "0.01".

And the third place is called the "thousandths", which represents a place value of $\frac{1}{1000}$ of the whole or one-thousandth of the whole. In numerical form, this decimal fraction is written as "0.001".

Examples

1. 25.678

The whole part is 25

The place value of the decimal part are:

6 → tenths
7 → hundredths
8 → thousandths

Types of Decimals

Based on the number of digits after the decimal point, the decimal numbers can be divided into two categories:

Like decimals: Two decimal numbers are said to be "like" decimals if they have the same number of digits after the decimal point. For example, 6.34 and 2.67 both have two digits after the decimal point so they are Like decimals.

Unlike decimals: Two decimal numbers are said to be "unlike" decimals if they have different number of digits after the decimal point. For example, 5.3 and 6.873 both have different number of digits after the decimal point so they are unlike decimals.

Rounding off decimal numbers

Decimals are rounded to a number of digit(s) after the decimal point (.)

1 digit after the decimal point is called one decimal place or nearest tenths
2 digits after the decimal point is called two decimal places or nearest hundredths
3 digits after the decimal point is called three decimal places or nearest thousandths
4 digits after the decimal point is called four decimal places or nearest ten thousandths
5 digits after the decimal point is called five decimal places or nearest hundred thousandths
and so on

To round a number look at the next digit in the right place, if the digit is less than 5, round down (maintain the digit at where you are rounding to) and if the digit is 5 or more than 5, round up (add 1 to the digit where you are rounding to).

Examples

1. Round 542.33 to the nearest tenths

Nearest tenths is 1 digit after the decimal point.

The digit after the decimal point is 3

The digit next to it is 3 which is less than 5, hence we maintain the digit at the tenth

542.33 to the nearest tenths = 542.3

2. Round 542.33 to one decimal place

This question is the same as question 1. One decimal place is the same as the nearest tenth.

542.33 to one decimal place is 542.3

3. Round 46.1438 to the nearest hundredths

Nearest hundredths is two digits after the decimal point (two decimal places).

The second digit after the decimal point is 4

The digit after the second digit is 3 which is less than 5, hence the second digit after the decimal point is maintained.

46.1438 to the nearest hundredths = 46.14

4. Round 4.21652 to the nearest thousandths.

The nearest thousandths is three digits after the decimal point.

The third digit after the decimal point is 6.

The next digit after the third digit is 5 which is more than 5, hence 1 is added to the third digit (6) making 1+6 = 7

4.21652 to the nearest thousandths = 4.217

5. Round 0.32721 to two decimal places.

Two decimal places is the second digit after the decimal point which 2

The digit after the second digit is 7 which is more than 5, hence 1 is added to the second digit (2) making 2+1 = 3

0.32721 to two decimal places = 0.33

Rounding off decimals to the nearest whole numbers

To round off decimals to the nearest whole number follow the steps below:

1. Look at the digit after the decimal point (the tenth place)
2. If the digit is less than 5, the whole number part of the decimal is maintained as the nearest whole number
3. If the digit (tenth place) is 5 or more, add 1 to the whole number part

Examples

1. Round 945.65 to the nearest whole number.

The whole number part is 945

The digit at the tenth part is 6 which is more than 5, hence we add 1 to the whole number part making 945 + 1 = 946

945.65 to the nearest whole number = 946

2. A bag of rice weighs 27.51 kg. What is his weight to the nearest kg?

The whole number part is 27

The digit at the tenth part is 5, hence we add 1 to the whole number part making 27 + 1 = 28

27.51 kg to the nearest kg = 28

3. Round 145.25 to the nearest whole number.

The whole number part is 145

The tenth part is 2 which is less than 5, hence the whole number part is maintained.

Round 145.25 to the nearest whole number is 145

4. Round 0.5 to the nearest whole number.

The whole number part is 0

The tenth part is 5, hence we add 1 to the whole number part making 0 + 1 = 1

0.5 to the nearest whole number = 1

APPLICATION OF KNOWLEDGE

Question 9

What is the value of the digit 9 in the number 624.93?

A. 9 hundreds B. 9 tens C. 9 units D. 9 tenths

[B.E.C.E 2006 Section A Question 36]

Solution

Question 10

What is the place value of 7 in 24.376?

A. Unit B. Ten C. Tenth D. Hundredth

[B.E.C.E 2015 Section A Question 4]

Solution

Question 11

Correct 5178.3426 to two decimal places.

A. 5178.00 B. 5178.30 C. 5178.34 D. 5178.35

[B.E.C.E 2016 Section A Question 11]

Solution