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1) 43.123456789

2) 0.120120012000120000…

3) 43.123456789123456789...

Answer :

1) 43.123456789

\(\Rightarrow \) \(43.123456789 = {43123456789 \over {10^9}} = {43123456789 \over {2^9 × 5^9}}\)

The above expression has denominator of the form \(2^n × 5^m\) where n and m are non-negative integers.

So, the number is a rational number, a terminating decimal number.

2) .0.120120012000120000…

Since,the given number is a non terminating non repeating number, it is not rational.

3) 43.123456789123456789....

The number is a rational number because decimal expansion is non terminating repeating.

It has denominator of the form \(2^n × 5^m\) where n and m are non-negative integers.

- Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. i.\({13 \over {3125}}\)ii.\({17 \over {8}}\)iii.\({64 \over {455}}\)iv.\({15 \over {1600}}\)v. \({29 \over {343}}\)vi.\({23 \over {2^3 × 5^2}}\)vii.\({{129} \over{2^2 × 5^7 × 7^5}}\)viii.\({6 \over {15}}\)ix.\({35 \over {50}}\) x.\({77 \over {210}}\)
- Write down the decimal expansions of those rational numbers in Question 1 which have terminating decimal expansions.

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