Skoool Kerala

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, 1000, and so on.

Decimal Places

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

For example, 3.42 = 3.4 to 1 decimal place (1 d.p.)

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 1 d.p.

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

47.3948 = 47.39 to 2 d.p.

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 point 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 1 d.p.

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

4) Significant figures (s.f.)

Examples for whole numbers

129 = 100 to 1 s.f.

129 = 130 to 2 s.f.

3684 = 3680 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.

45793 = 50000 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