Approximations

Rounding off Whole Numbers to Given Place Values

Round off whole numbers to given place values

STEPS

• When rounding a number, stand at the digit of the required place value, then look at the next digit to the right; if it is or more, round up (i.e, increase the digit of the required place value by 1) and if it is or less, do not change the digit of the required place value
• Replace all the remaining digits to the right of the required place value with the zeros

Example

Round off whole numbers to given place values

1. million
2. ten million

Solution

1. The million digit is 2, since the next digit to the right is greater than 5, then we can increase 2 by 1 and put the remaining digits to the right of 2 zeros. There fore;42,850,671 ≈ 43,000,000
2. The ten million digit is 4, since the next digit to the right is less than 5, then we do not change 4 but we put the remaining digits to the right of 4 zeros. There fore;42,850,671 ≈ 40,000,000

Example

Round off whole numbers to given place values

Solution:

6 is in the thousands place. The number to the right of 6 is 1. Then 426143 is 426000 rounded off to thousands.

Decimals to a Given Number of Decimal Place

Round off decimals to a given number of decimal place

STEPS

• When rounding a decimal, stand at the digit of the required decimal place, then look at the next digit to the right; if it is or more, round up (i.e increase the digit of the required decimal by 1) and if it is or less, do not change the digit of the required decimal place
• Replace all the remaining digits to the right of the required decimal place with the zeros

NOTE

• The first digit after the decimal point is the first decimal place, the second digit after the decimal point is the second decimal place e.t.c
• Example 0.568 is the first decimal place and is the second decimal place

Example

Round off decimals to a given number of decimal place

1. 1 decimal place
2. 2 decimal places
3. 3 decimal places

Solution:

1. 0.24736≈ 0.2 (1 d.p)
2. 0.24736≈ 0.25 (2 d.p)
3. 0.24736≈ 0.247 (3 d.p)

Example

Round off decimals to a given number of decimal place

Solution: 58 x 61 ≈ 60 x 60 =3600

Significant Figures

Significant figures of a number - are the significant digits, counted from left of the number.The first significant figure must be non-zero; following significant figures may take any value.

A Number to a Given Number of Significant Figures

Write a number to a given number of significant figures

Is the number of significant digits including 0 if it is between the first and the last

Examples

1. 13 – has two significant figures
2. 709.43 – has five significant figures
3. 0.0004001 – has four significant figures

STEPS

• When rounding a number to a certain significant figure, stand at the digit of the required significant figure, then look at the next digit to the right; if it is or more, round up (i.e increase the digit of the required significant figure by 1) and if it is or less, do not change the digit of the required significant figure
• Replace all the remaining digits to the right of the required significant figure with the zeros

Example

Write a number to a given number of significant figures

1. 1 first significant figure
2. 2 significant figure
3. 3 significant figure

Solution

1. 50
2. 45
3. 45.3

Example

Write a number to a given number of significant figures

1. 2 first significant figure
2. 4 significant figure
3. 3 significant figure

Solution

1. 150 000
2. 146 400
3. 146 000

Approximations in Calculations

The Knowledge of Rounding Off of Numbers in Computations Involving Large Numbers and Small Numbers

Use the knowledge of rounding off of numbers in computations involving large numbers and small numbers

Approximation can be used in operation to check whether a calculation is correct or not, i.e in addition, subtraction, multiplication and divisione.g 446 x 45 = 20 070

The above calculation can be checked quickly whether it is correct or not by rounding each number to 1 significant figure and then multiply i.e 400 x 50 = 20 000

Therefore, the approximation of 20 000 is close to 20 0070 is correct.Before carrying an operation, each number in a calculation is rounded to 1 significant figure

Example

Use the knowledge of rounding off of numbers in computations involving large numbers and small numbers

Example

Use the knowledge of rounding off of numbers in computations involving large numbers and small numbers

Solution

32 × 580 ≈30×600 = 18 000

The approximate transport cost was 18 000/-

Example

Use the knowledge of rounding off of numbers in computations involving large numbers and small numbers

Solution: 10.12 x 0.08 = 0.8096 has 4 decimal places