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Fractions, Decimals, and Percentages - Decimals and place value

Grade 6IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Decimal Place Value: Understanding that digits to the right of the decimal point represent tenths (1/10), hundredths (1/100), and thousandths (1/1000).

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Comparing and Ordering: Decimals are compared by looking at digits from left to right, starting with the highest place value.

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Rounding Decimals: To round a decimal, look at the digit to the right of the target place; if it is 5 or greater, round up; if it is 4 or less, stay the same.

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Multiplying and Dividing by Powers of 10: Multiplying moves the decimal point to the right, while dividing moves it to the left.

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Terminal vs Recurring Decimals: Terminal decimals end (e.g., 0.25), whereas recurring decimals have a repeating pattern (e.g., 0.333...).

📐Formulae

Tenths=110=0.1\text{Tenths} = \frac{1}{10} = 0.1

Hundredths=1100=0.01\text{Hundredths} = \frac{1}{100} = 0.01

Thousandths=11000=0.001\text{Thousandths} = \frac{1}{1000} = 0.001

x×10n⇒x \times 10^n \Rightarrow Move decimal nn places to the right

x÷10n⇒x \div 10^n \Rightarrow Move decimal nn places to the left

💡Examples

Problem 1:

Identify the place value of the digit 7 in the number 45.07245.072.

Solution:

Hundredths (0.010.01)

Explanation:

In 45.07245.072, 4 is tens, 5 is units, 0 is tenths, 7 is hundredths, and 2 is thousandths.

Problem 2:

Round 12.64812.648 to one decimal place.

Solution:

12.612.6

Explanation:

The digit in the first decimal place is 6. The digit to its right is 4. Since 4 is less than 5, we keep the 6 and drop the remaining digits.

Problem 3:

Calculate 3.45×1003.45 \times 100.

Solution:

345345

Explanation:

Multiplying by 100 means moving the decimal point two places to the right (since 100 has two zeros).

Problem 4:

Arrange these decimals in ascending order: 0.4,0.045,0.440.4, 0.045, 0.44.

Solution:

0.045,0.4,0.440.045, 0.4, 0.44

Explanation:

To compare, equalize the number of decimal places: 0.400,0.045,0.4400.400, 0.045, 0.440. 0.0450.045 is the smallest, followed by 0.4000.400, then 0.4400.440.