Express 1.53: Complete the Decimal Expression

Q: Why is the denominator 100 and not 53?

The denominator comes from place value, not the digits themselves! Since .53 has digits in the hundredths place, we use 100 as the denominator. The 53 becomes the numerator.

Q: What if I want to simplify the fraction further?

Great thinking! $ \frac{53}{100} $ cannot be simplified because 53 and 100 share no common factors other than 1. So $ 1\frac{53}{100} $ is already in simplest form.

Q: How do I know which place value I'm working with?

Count the decimal places! One decimal place = tenths (denominator 10). Two decimal places = hundredths (denominator 100). Three decimal places = thousandths (denominator 1000).

Q: Can I write this as an improper fraction instead?

Yes! $ 1\frac{53}{100} = \frac{100 + 53}{100} = \frac{153}{100} $. Both forms are correct, but the question asks for the mixed number format.

Q: What's the difference between 1.53 and 1.5?

$ 1.53 = 1\frac{53}{100} $ while $ 1.5 = 1\frac{5}{10} = 1\frac{50}{100} $. The extra digit in the hundredths place makes a significant difference in value!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to mixed fraction

00:03 Break down the number into whole number and remainder

00:08 Convert the remainder to fraction

00:16 Combine into mixed fraction

00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$1.53=$

2

Step-by-step solution

To convert $1.53$ into a fraction with 100 as the denominator, follow these steps:

Step 1: Identify the whole number and the decimal part of $1.53$ .
Step 2: The whole number part is $1$ .
Step 3: The decimal part ".53" represents $\frac{53}{100}$ because the decimal extends to the hundredth place.
Step 4: Combine the whole number and fraction to write $1.53$ as a mixed number: $1\frac{53}{100}$ .

Thus, $1.53$ converted to a mixed number with a denominator of 100 is $1\frac{53}{100}$ .

3

Final Answer

$1\frac{53}{100}$

Key Points to Remember

Essential concepts to master this topic

Place Value: Hundredths place means denominator of 100
Technique: Convert .53 to $\frac{53}{100}$ using place value
Check: Verify $1\frac{53}{100} = 1 + 0.53 = 1.53$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on digits count
Don't use 10 as denominator just because .53 has two digits = $1\frac{53}{10} = 6.3$ which is wrong! The decimal .53 goes to hundredths place, not tenths. Always use denominator 100 for two decimal places.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

Why is the denominator 100 and not 53?

+

The denominator comes from place value, not the digits themselves! Since .53 has digits in the hundredths place, we use 100 as the denominator. The 53 becomes the numerator.

What if I want to simplify the fraction further?

+

Great thinking! $\frac{53}{100}$ cannot be simplified because 53 and 100 share no common factors other than 1. So $1\frac{53}{100}$ is already in simplest form.

How do I know which place value I'm working with?

+

Count the decimal places! One decimal place = tenths (denominator 10). Two decimal places = hundredths (denominator 100). Three decimal places = thousandths (denominator 1000).

Can I write this as an improper fraction instead?

+

Yes! $1\frac{53}{100} = \frac{100 + 53}{100} = \frac{153}{100}$ . Both forms are correct, but the question asks for the mixed number format.

What's the difference between 1.53 and 1.5?

+

$1.53 = 1\frac{53}{100}$ while $1.5 = 1\frac{5}{10} = 1\frac{50}{100}$ . The extra digit in the hundredths place makes a significant difference in value!

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Express 1.53: Complete the Decimal Expression

Mixed Numbers with Hundredths Place

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