Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Understanding the Decimal Point: The decimal point separates the whole number part from the fractional part.
Place Value Positions: Digits to the right of the decimal point represent Tenths (1/10), Hundredths (1/100), and Thousandths (1/1000).
Value of Digits: In the number 0.582, '5' is 5 tenths, '8' is 8 hundredths, and '2' is 2 thousandths.
Expanded Form: Writing a decimal as the sum of its parts (e.g., ).
Comparing Decimals: To compare, align the decimal points and compare digits from left to right (tenths, then hundredths, then thousandths).
Rounding: To round to the nearest hundredth, look at the thousandths digit; if it is 5 or more, round up.
📐Formulae
💡Examples
Problem 1:
Identify the place value of the digit 7 in the number 12.473.
Solution:
Hundredths
Explanation:
In 12.473, 4 is in the tenths place, 7 is in the hundredths place, and 3 is in the thousandths place.
Problem 2:
Write the decimal 0.045 as a fraction in its simplest form.
Solution:
Explanation:
0.045 has three decimal places, so it is . Dividing both the numerator and denominator by 5 gives .
Problem 3:
Which number is greater: 0.509 or 0.51?
Solution:
0.51
Explanation:
Compare the digits. Both have 0 wholes and 5 tenths. In the hundredths place, 0.51 has 1, while 0.509 has 0. Since 1 > 0, 0.51 is greater (you can also think of 0.51 as 0.510).
Problem 4:
Round 3.1415 to the nearest thousandth.
Solution:
3.142
Explanation:
The thousandths digit is 1. The digit to its right (ten-thousandths) is 5. Since it is 5 or greater, we increase the thousandths digit by 1.