Module 1 (M1) - Number & algebra - Decimals

Decimals

Counting decimal places

Three point seven two eight. Seven is labelled ‘First decimal place’. Two is labelled ‘Second decimal place’. Eight is labelled ‘Third decimal place’. — Image caption,
Decimal places are counted from the decimal point. The number 3 ∙728 is written to three decimal places.

The number 5.714 has three decimal places – 3 digits after the decimal point.

The number 23.4275 has four decimal places while 674.4 has one decimal place.

Rounding to a number of decimal places

Rounding to one decimal place

Look at the second digit after the decimal point

If that digit is 5 or more, add one to the number in the first decimal place
If that digit is less than 5, the number in the first decimal place stays the same

Rounding to two decimal places

Look at the third digit after the decimal point

If that digit is 5 or more, add one to the number in the second decimal place
If that digit is less than 5, the number in the second decimal place stays the same

Example

Ruby divides 61 by 7 on her calculator. The display shows 8.71428571

Round this answer to one decimal place.

Solution: The second digit after the decimal point is ‘1’ (less than 5) so the digit in the first decimal place stays the same.

Answer: 8.7

Example

When 23.15 is divided by 17, the calculator display shows 1.36176470

Write this answer to three decimal places.

Solution: The 4th digit after the decimal point is ‘7’ (more than 5) so add 1 to the digit in the 3rd decimal place.

Answer: 1∙362

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Round 8∙736 to 2 decimal places. This means starting at 2 digits after the decimal point. Count the digits from the decimal point. The digit 3 is in the second decimal place.
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The next digit is 6. Because 6 is more than 5, the 3 is rounded up. 8∙736 rounded to 2 decimal places is 8∙74
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Round 6∙8279 to 1 decimal place. This means starting at 1 digit after the decimal point. Count the digits from the decimal point. 8 is in the first decimal place.
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The next digit is 2. Because 2 is less than 5, the 8 in the second decimal place is not changed. 6∙8279 to 1 decimal place is rounded down to 6∙8.
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Round 4∙8298 to 3 decimal places. This means starting at 3 digits after the decimal point. Count the digits from the decimal point. 9 is in the third decimal place.
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The next digit after the third decimal place is 8. Because 8 is more than 5, the 9 is rounded up. However, the 9 cannot be rounded up to 10. The number must be rounded to 4∙830

Activity

Question

How many decimal places does the number 12.725 have?

Question

Divide 14 by 13 and give your answer correct to three decimal places.

Question

Ryan divides 0.998 by 5 and gets an answer of 0.1996.

Round this answer to two decimal places.

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