0.0909 Repeating As A Fraction

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Write the following in decimal form and say what kind of decimal expansion each has: i) 36/100 2) 1/xi 3)\(four{\Large\frac{ane}{8}}\) 4) 3/13 5) 2/11 six) 329/400

Solution:

i) 36/100

36/100 = 0.36

Thus, 36/100 in decimal format is represented every bit 0.36.

This is a terminating decimal number.

2) 1/11

The residue 1 keeps repeating. And then, 1/11 = 0.0909… and it can be written as 1/11 =
0.09

This is a non-terminating recurring decimal.

iii)
\(iv{\Large\frac{i}{8}}\)

\(iv{\Large\frac{1}{viii}}\) tin can be expressed as 33/8 in terms of improper fraction.

Write the following in decimal form and say what kind of decimal expansion each has: i) 36/100 ii) 1/11 iii)4 1/8 iv) 3/13 v) 2/11 vi) 329/400

Thus,
\(iv{\Big\frac{one}{8}}\)
= 33/eight = 4.125

Thus,
\(4{\Big\frac{1}{8}}\)
in decimal grade is written as 4.125.

This is a terminating decimal number because the residual is nix.

four) three/13

Thus, 3/xiii = 0.23076923…

We see that the prepare of numbers 230769 after the decimal point keeps repeating. So, this is a non-terminating recurring decimal.

v) 2/11

Write the following in decimal form and say what kind of decimal expansion each has: i) 36/100 ii) 1/11 iii)4 1/8 iv) 3/13 v) 2/11 vi) 329/400

Thus, 2/11 = 0.1818

Here, we meet that the block of numbers 18 keeps repeating. Hence, this is a non-terminating recurring decimal.

vi) 329/400

329/400 = 329 ÷ (iv × 100) = 0.8225

Write the following in decimal form and say what kind of decimal expansion each has: i) 36/100 ii) 1/11 iii)4 1/8 iv) 3/13 v) 2/11 vi) 329/400

Now, 82.25/100 = 0.8225

Thus, 329/400 in decimal form is written as 0.8225.

This is a terminating decimal number because the residuum is nix.

☛ Bank check:
NCERT Solutions for Course 9 Maths Chapter 1

Video Solution:

Write the following in decimal form and say what kind of decimal expansion each has: i) 36/100 ii) 1/11 iii)
\(iv{\Large\frac{one}{viii}}\) iv) 3/13 five) 2/11 vi) 329/400

NCERT Solutions Course 9 Maths Chapter 1 Do 1.iii Question one

Summary:

We see that in decimal course 36/100,
\(4{\Large\frac{1}{eight}}\), 329/400 are terminating decimals, whereas 1/eleven, iii/xiii, 2/11 are not-terminating recurring decimal.

☛ Related Questions:

You know that 1/seven = 0.142587. Tin can you predict what the decimal expansions of two/7, 3/seven, four/seven, 5/7, six/7 are, without actually doing the long segmentation? If so, how?
Express the following in the class of p/q, where p and q are integers and q ≠ 0. i) 0.half dozen ii) 0.47 3) 0.001
Express 0.99999 …. in the form of p/q. Are yous surprised with your respond? With your teacher and classmates discuss why the answer makes sense?
What tin be the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.

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