Convert Decimal 1.77: Finding Equivalent Number Representations

Q: Why is the denominator 100 and not 10?

Count the decimal places! $ 1.77 $ has two digits after the decimal point (7 and 7), so it represents hundredths. Two decimal places always means the denominator is 100.

Q: Do I include the whole number part in the numerator?

Yes! Convert the entire decimal to an improper fraction. $ 1.77 = \frac{177}{100} $ because 1.77 means 177 hundredths total.

Q: What if I want to write it as a mixed number?

You can! $ \frac{177}{100} = 1\frac{77}{100} $. Divide: 177 ÷ 100 = 1 remainder 77, so it's 1 and 77/100.

Q: How do I remember which denominator to use?

1 decimal place → tenths → denominator 102 decimal places → hundredths → denominator 1003 decimal places → thousandths → denominator 1000The pattern is: denominator = 10^(number of decimal places)

Decimal to Fraction with Hundredths Place

Convert into fraction form:

$1.77=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 Match the position of digits after the decimal point to the appropriate division

00:06 Place the digits in the numerator, and the appropriate division in the denominator

00:11 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert into fraction form:

$1.77=$

Step-by-step solution

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

We will write the fraction in the following way:

$\frac{177}{100}$

Final Answer

$\frac{177}{100}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Two decimal places means denominator is 100
Technique: Write 1.77 as 177/100 using all digits without decimal
Check: Divide 177 ÷ 100 = 1.77 to verify conversion ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal places
Don't use 10 as denominator for 1.77 = 177/10 = 17.7! This ignores the hundredths place value. The decimal 1.77 has TWO places after the decimal point. Always count decimal places: one place = tenths (÷10), two places = hundredths (÷100).

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 10?

Count the decimal places! $1.77$ has two digits after the decimal point (7 and 7), so it represents hundredths. Two decimal places always means the denominator is 100.

Do I include the whole number part in the numerator?

Yes! Convert the entire decimal to an improper fraction. $1.77 = \frac{177}{100}$ because 1.77 means 177 hundredths total.

What if I want to write it as a mixed number?

You can! $\frac{177}{100} = 1\frac{77}{100}$ . Divide: 177 ÷ 100 = 1 remainder 77, so it's 1 and 77/100.

Can this fraction be simplified?

Check if 177 and 100 share common factors. Since 177 = 3 × 59 and 100 = 2² × 5², they share no common factors, so $\frac{177}{100}$ is already in lowest terms.

How do I remember which denominator to use?

1 decimal place → tenths → denominator 10
2 decimal places → hundredths → denominator 100
3 decimal places → thousandths → denominator 1000

The pattern is: denominator = 10^(number of decimal places)

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