CONVERTING THE DECIMALS AS FRACTION

Here we see how to convert the terminating decimals to fraction.

To convert terminating decimal to fraction,

  • We have to notice, the number of digits after the decimal.
  • Based on the number of digits after the decimal, we may have to choose 10, 100, 1000, ...... etc.
  • Multiply the numerator and denominator by 10n. Here n will represent the number of digits after the decimal.
  • After we get rid of the decimal and made it as integer at the numerator, we can move the decimal backwards n digits.

Change the following decimal numbers to fractions or mixed numbers. Reduce answers, if possible.

Problem 1 :

0.25

Solution :

Number of digits after the decimal point is 2.

So, we  have to multiply both numerator and denominator by 100.

= 0.251 × 100100= 25100= 14

Problem 2 :

0.2

Solution :

Number of digits after the decimal point is 1.

So, we  have to multiply both numerator and denominator by 10.

= 0.21 × 1010= 210= 15

Problem 3 :

3.8

Solution :

Number of digits after the decimal point is 1.

So, we  have to multiply both numerator and denominator by 10.

= 3.81 × 1010= 3810= 195= 3 45

Problem 4 :

0.75

Solution :

Number of digits after the decimal point is 2.

So, we  have to multiply both numerator and denominator by 100.

= 0.751 × 100100= 75100= 34

Problem 5 :

0.16

Solution :

Number of digits after the decimal point is 2.

So, we  have to multiply both numerator and denominator by 100.

= 0.161 × 100100= 16100= 425

Problem 6 :

0.625

Solution :

Number of digits after the decimal point is 3.

So, we  have to multiply both numerator and denominator by 1000.

= 0.6251 × 10001000= 6251000= 58

Problem 7 :

16.31

Solution :

Number of digits after the decimal point is 2.

So, we  have to multiply both numerator and denominator by 100.

= 16.311 × 100100= 1631100= 16 31100

Problem 8 :

3.35

Solution :

Number of digits after the decimal point is 2.

So, we  have to multiply both numerator and denominator by 100.

= 3.351 × 100100= 335100= 6720= 3 720

Problem 9 :

0.07

Solution :

Number of digits after the decimal point is 2.

So, we  have to multiply both numerator and denominator by 100.

= 0.071 × 100100= 7100

Problem 10 :

0.1875

Solution :

Number of digits after the decimal point is 4.

So, we  have to multiply both numerator and denominator by 10000.

= 0.18751 × 1000010000= 187510000= 316

Problem 11 :

42.325

Solution :

Number of digits after the decimal point is 3.

So, we  have to multiply both numerator and denominator by 1000.

= 42.3251 × 10001000= 423251000= 169340= 42 1340

Problem 12 :

7.37

Solution :

Number of digits after the decimal point is 2.

So, we  have to multiply both numerator and denominator by 100.

= 7.371 × 100100= 737100= 7 37100

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