Converting a decimal to a proper fraction in simplest form: Advanced Online Quiz

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Questions and Answers
Q 1 - Convert the decimal 0.265 to a proper fraction in simplest form.

Answer : A

Explanation

Step 1:

We drop the decimal and write the number 265 as the top of a fraction.

Step 2:

The place value of the last digit 5, is a thousandth. So, we take 1000 as the bottom of the fraction to get $0.265 = \frac{265}{1000}$

Step 3:

To reduce the fraction to the simplest form, we divide the top and bottom of the fraction with the highest common factor of 265 and 1000 which is 5

$\frac{(265 \div 5)}{(1000 \div 5)} = \frac{53}{200}$

Step 4:

So, $0.265 = \frac{53}{200}$

Q 2 - Convert the decimal 0.272 to a proper fraction in simplest form.

Answer : C

Explanation

Step 1:

We drop the decimal and write the number 272 as the top of a fraction.

Step 2:

The place value of the last digit 2, is a thousandth. So, we take 1000 as the bottom of the fraction to get $0.272 = \frac{272}{1000}$

Step 3:

To reduce the fraction to the simplest form, we divide the top and bottom of the fraction with the highest common factor of 272 and 1000 which is 8

$\frac{272 \div 8}{1000 \div 8} = \frac{34}{125}$

Step 4:

So, $0.272 = \frac{34}{125}$

Q 3 - Convert the decimal 0.288 to a proper fraction in simplest form.

Answer : B

Explanation

Step 1:

We drop the decimal and write the number 288 as the top of a fraction.

Step 2:

The place value of the last digit 8, is a thousandth. So, we take 1000 as the bottom of the fraction to get $0.288 = \frac{288}{1000}$

Step 3:

To reduce the fraction to the simplest form, we divide the top and bottom of the fraction with the highest common factor of 288 and 1000 which is 8

$\frac{(288 \div 8)}{1000 \div 8} = \frac{36}{125}$

Step 4:

So, $0.288 = \frac{36}{125}$

Q 4 - Convert the decimal 0.316 to a proper fraction in simplest form.

Answer : D

Explanation

Step 1:

We drop the decimal and write the number 316 as the top of a fraction.

Step 2:

The place value of the last digit 6, is a thousandth. So, we take 1000 as the bottom of the fraction to get $0.316 = \frac{316}{1000}$

Step 3:

To reduce the fraction to the simplest form, we divide the top and bottom of the fraction with the highest common factor of 316 and 1000 which is 4

$\frac{316 \div 4}{1000 \div 4} = \frac{79}{250}$

Step 4:

So, $0.316 = \frac{79}{250}$

Q 5 - Convert the decimal 0.354 to a proper fraction in simplest form.

Answer : B

Explanation

Step 1:

We drop the decimal and write the number 354 as the top of a fraction.

Step 2:

The place value of the last digit 4, is a thousandth. So, we take 1000 as the bottom of the fraction to get $0.354 = \frac{354}{1000}$

Step 3:

To reduce the fraction to the simplest form, we divide the top and bottom of the fraction with the highest common factor of 354 and 1000 which is 2

$\frac{354 \div 2}{1000 \div 2} = \frac{177}{500}$

Step 4:

So, $0.354 = \frac{177}{500}$

Q 6 - Convert the decimal 0.384 to a proper fraction in simplest form.

Answer : C

Explanation

Step 1:

We drop the decimal and write the number 384 as the top of a fraction.

Step 2:

The place value of the last digit 4, is a thousandth. So, we take 1000 as the bottom of the fraction to get $0.384 = \frac{384}{1000}$

Step 3:

To reduce the fraction to the simplest form, we divide the top and bottom of the fraction with the highest common factor of 384 and 1000 which is 8

$\frac{384 \div 8}{1000 \div 8} = \frac{48}{125}$

Step 4:

So, $0.384 = \frac{48}{125}$

Q 7 - Convert the decimal 0.428 to a proper fraction in simplest form.

Answer : A

Explanation

Step 1:

We drop the decimal and write the number 428 as the top of a fraction.

Step 2:

The place value of the last digit 8, is a thousandth. So, we take 1000 as the bottom of the fraction to get $0.428 = \frac{428}{1000}$

Step 3:

To reduce the fraction to the simplest form, we divide the top and bottom of the fraction with the highest common factor of 428 and 1000 which is 4

$\frac{428 \div 4}{1000 \div 4} = \frac{107}{250}$

Step 4:

So, $0.428 = \frac{107}{250}$

Q 8 - Convert the decimal 0.472 to a proper fraction in simplest form.

Answer : D

Explanation

Step 1:

We drop the decimal and write the number 472 as the top of a fraction.

Step 2:

The place value of the last digit 2, is a thousandth. So, we take 1000 as the bottom of the fraction to get $0.472 = \frac{472}{1000}$

Step 3:

To reduce the fraction to the simplest form, we divide the top and bottom of the fraction with the highest common factor of 472 and 1000 which is 8

$\frac{472 \div 8}{1000 \div 8} = \frac{59}{125}$

Step 4:

So, $0.472 = \frac{59}{125}$

Q 9 - Convert the decimal 0.576 to a proper fraction in simplest form.

Answer : A

Explanation

Step 1:

We drop the decimal and write the number 576 as the top of a fraction.

Step 2:

The place value of the last digit 6, is a thousandth. So, we take 1000 as the bottom of the fraction to get $0.576 = \frac{576}{1000}$

Step 3:

To reduce the fraction to the simplest form, we divide the top and bottom of the fraction with the highest common factor of 576 and 1000 which is 8

$\frac{576 \div 8}{1000 \div 8} = \frac{72}{125}$

Step 4:

So, $0.576 = \frac{72}{125}$

Q 10 - Convert the decimal 0.726 to a proper fraction in simplest form.

Answer : C

Explanation

Step 1:

We drop the decimal and write the number 726 as the top of a fraction.

Step 2:

The place value of the last digit 6, is a thousandth. So, we take 1000 as the bottom of the fraction to get $0.726 = \frac{726}{1000}$

Step 3:

To reduce the fraction to the simplest form, we divide the top and bottom of the fraction with the highest common factor of 726 and 1000 which is 2

$\frac{726 \div 2}{1000 \div 2} = \frac{363}{500}$

Step 4:

So, $0.726 = \frac{363}{500}$

converting_decimal_to_proper_fraction_in_simplest_form_advanced.htm
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