Removing extra zeros from decimal numbers
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Students learn when a zero is extra in decimal numbers and which they can remove.
It is important to know that some zeros are extra in decimal numbers and can be removed. Zero as a placeholder is important, but zero without meaning can be removed without changing the number at all.
Show the image of the speed skater and the stopwatch with the time of 32.10 seconds. Ask how fast the speed skater is, and what the 32.10 exactly means. It is 32 whole seconds, 1 tenth and 0 hundredths (or just ten hundredths).
Explain that it is important to learn to recognize which zeros in decimal numbers are extra- zero as a placeholder is important, but an extra zero has no meaning and can be removed from a number. Explain that a 0 that is set after(to the right) of a number changes the number. 1 and 10 and 100 and 1,000 are all different numbers with 0 acting as a placeholder and showing value. Next explain that a 0 that is set before (to the left) of a whole number does not change the number. 1 and 01 are both 1. As such, the zeros before the whole numbers can be removed. Following this explanation with whole numbers, you now show the decimal numbers. Show students that a zero that comes after the decimal point, but before a number changes the value- with 0.1, 0.01, and 0.001 the zero is a placeholder to show value. The next slide shows that when a zero comes after the decimal point and there are no more numbers, it is extra and can be removed. Practice dragging the extra zeros from numbers with 4 digits to the box with the students. Repeat this with a decimal number with six digits. Emphasize that the zero is only extra when it does not act as a placeholder for another number. Show the students the number with eight digits and ask them to write the number without extra zeros down. Have them hold up their answers to check their work.
Check that students understand how to recognize extra zeros and then to remove extra zeros from decimal numbers by asking the following questions:
- Why are some zeros extra in decimal numbers?
- How do you know if a zero is extra and can be removed?
Students first get exercises where they choose from multiple choice answers. Next they get decimal numbers with seven digits and need to choose which number is left when you remove the extra zeros. They repeat this with a number with eight digits.
Discuss the goal of recognizing and removing extra zeros from decimal numbers with your students. Make sure they know to check if zero is acting as a placeholder or not to help determine if a zero can be removed or not. Ask students to form pairs. Have both students write five decimal numbers with a maximum of ten digits. They trade papers and must cross out the extra zeros in the numbers their partner created. The students can compete to see who correctly finishes first.
Students who have difficulty with recognizing and removing extra zeros can be supported by extra discussion of tenths, hundredths and thousandths. By showing how the zeros in 0.01 (and other decimal numbers) act as placeholders and comparing them to 01.00 in which the zeros do nothing, it can help support learning which zeros are extra.
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