Comparing Decimals on a Number Line

Comparing Decimals on a Number Line exercise

• What is a decimal number?

  Hints

  Think about a number that has a part before and after a dot (for example, 3.14).

  The dot in a decimal number is called a decimal point, which separates the whole number from the fractional part.

  Solution

  A decimal number is a representation of numbers that include a whole number and a fractional part, separated by a decimal point.

  The fractional part can extend to tenths, hundredths, thousandths and beyond.

• Which of the following numbers is greater: 2.27 or 2.7?

  Hints

  If the digits in the ones place are the same, look at the digits in the tenths place.

  Look at the digits to the right of the decimal point to compare which is bigger.

  Solution

  2.7 > 2.27.

  Compare the whole number parts: Both numbers have the same whole number part, which is 2.

  Compare the tenths place: In 2.27, the digit in the tenths place is 2. In 2.7, the digit in the tenths place is 7.

  Since 7 > 2, 2.7 > 2.27.

• Compare the decimals and place them on the number line.

  Hints

  Start by comparing the digits in the tenths place if the ones place digits are the same.

  Compare the tenths digits, 1 in 4.143, 4 in 4.458 and 7 in 4.765.

  Solution

  Here we can see the numbers placed correctly on the number line.

  Compare the ones place: All numbers have the same ones place, which is 4.

  Compare the tenths place: In 4.143, the digit in the tenths place is 1, in 4.458, the digit in the tenths place is 4 and in 4.765, the digit in the tenths place is 7.

  Since 7 > 4 > 1, 4.765 > 4.458 > 4.143.

• Place the decimals in order from smallest to largest on the number line.

  Hints

  Compare the digits from left to right, starting with the ones place.

  If the digits in one place value are the same, move to the next place value to determine the order.

  You could add a 0 to the end of 5.82 and 5.89 so they all have three digits after the decimal point to help with comparing.

  Solution

  The correct order is: 5.801, 5.82, 5.89.

  Steps:

  1. Compare ones place: All numbers start with 5, so they're the same.

  2. Compare tenths place:

  5.82 has an 8

  5.801 has an 8

  5.89 has an 8

  3. Compare hundredths place:

  5.82 has a 2

  5.801 has a 0

  5.89 has a 9

  So, 0 is smallest, 2 is in the middle and 9 is the largest.

  You can stop comparing after step 3.

• You are comparing the lengths of two ribbons.

  Hints

  Compare the digits in the ones place first.

  If they are the same, then compare the digits in the tenths place.

  Look at the tenths place: compare 4 in 2.45 and 5 in 2.54.

  Which one is greater?

  Solution

  The ribbon that is 2.54 metres long is longer.

• Which fruit is the heaviest?

  Hints

  Start by comparing the digits in the ones place, then move to the tenths, hundredths and thousandths places step by step.

  If the digits are the same, move to the next place value to determine the larger number.

  If you compare the digits in the hundredths place, you will see that two pieces of fruit are heavier than the other two.

  Once you have found the two heaviest pieces of fruit, compare the digits in the thousandths place.

  Solution

  The banana is the heaviest, with a weight of 0.176 kg.

  Compare the tenths place:

  • All pieces of fruit have the same tenths digit (1), so move to the next digit.

  • Compare the hundredths place:

  Apple: 7

  Banana: 7

  Kiwi: 6

  Orange: 6

  The banana and apple both have 7, but we need to check the next digit for both to be sure.

  • Compare the thousandths place for banana and apple:

  Banana: 6

  Apple: 2

  The banana has the larger thousandths digit (6 > 2).