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Decimal Places, Significant Figures and Estimates

Approximate Values | Decimal Places | Significant Figures | Estimates

Approximate Values

To write an approximate value for a number, we can use several methods.

1) Rounding to the nearest whole number

2,4 = 2 to the nearest whole number, because it is nearer to 2 than to 3.

76,2 = 76 to the nearest whole number, because it is nearer to 76 than to 77.

7,8 = 8 to the nearest whole number, because it is nearer to 8 than to 7.

Rule: If the digit after the units is 5 or more, then round up the units. Otherwise leave the units as they are. Note the decimal part is left off.

2) Rounding to the nearest ten

13 = 10 (to the nearest ten)

68 = 70 (to the nearest ten)

25 = 30 (to the nearest ten)

Rule: If the digit after the tens is 5 or more then round up the tens.

In the same way we can round to the nearest 100, 1 000, and so on.

1 467	= 1 000 to the nearest 1 000.
	= 1 500 to the nearest 100.

Decimal Places

We use similar rules as above but we start counting after the decimal comma.

For example, 3,42 = 3,4 to one decimal place.

One decimal place is the first figure after the point. Because it is followed by a 2, it stays the same.

6,58 = 6,6 to one decimal place.

Because the 5 is followed by an 8 it is rounded to a 6.

47,3948 = 47,39 to two decimal places.

The 9 is the second decimal place, followed by a number less than 5, so it stays the same.

Rule: Count the figures after the comma to find the decimal place. If this is followed by a number less than 5, it stays as it is. Otherwise it is rounded up.

3,98 = 4,0 to one decimal place.

Because the 9 is rounded up to a 10 which makes the 3 into a 4. Note the 0 is needed this time.

Significant Figures

Examples for whole numbers

129 = 100 to 1 s.f.

129 = 130 to 2 s.f.

3 684 = 3 680 to 3 s.f.

Note: We start counting from the first figure in the number. Figures left off must be replaced by zeros, otherwise we lose the place value.

45 793 = 50 000 to 1 s.f.

Examples for decimals

0,0047 = 0,005 to 1 s.f.

Note: We start counting from the first non-zero figure.

0,07649 = 0,076 to 2 s.f.

Figures left off are not replaced by zeros.

Estimates

When estimating the answer to a calculation we round off the numbers to 1 s.f. We then use the closest convenient number in order to make the calculation as simple as possible.

Example: Estimate the value of 19,6 ÷ 3,28.

19,6 = 20
3,28 = 3	(to 1 s.f.)

19,6 ÷ 3,28 = 20 ÷ 3	(to 1 s.f.)
21 ÷ 3 = 7	(21 being more convenient)
The estimate is 7.

Note: Estimates should always be used when doing calculations on the calculator, to check the answer. They can also be asked as specific questions on the exam paper.