Page 6-9 Review (Fractions, Decimals, %’s)
1.) Explain how it is easy to order numbers from least to greatest when they are all in scientific
notation form. Just look at the exponent 1st. If the exponents are the same then look at the
number.
2.) Explain when it is possible for ¼ to be bigger than ½ . This is possible when you have different
“whole” amounts. For example, a ¼ of a large pizza is bigger than ½ of some small pizzas.
3.) When changing a percent to a decimal, why do we divide by 100? We divide by 100 because the
“whole” in percent form is 100 times bigger than the whole in decimal form.
4.) When changing a decimal to a percent, why do we multiply by 100? The whole in decimal form
is 1 and the whole in percent form is 100(a hundred times bigger)
5.) Sally wants to use the shortcut for moving a percent to a decimal. She can’t remember whether
to move the decimal two spaces left or two spaces right. How would Sally having knowledge of
the “whole” in decimal form versus percent form help her use the short cut more effectively?
When moving a percent to decimal form we must move the decimal to the left because we need
a smaller number in decimal form. If Sally would have known percent form was bigger by 100
times she would know she needs to move the decimal left 2 spaces to make a smaller number
for decimal form.
6.) What do you need to do in order to put fractions, decimals, percents, and scientific notation in
order from least to greatest? The best thing to do would be to make all numbers decimal form.
You could also change everything to percent form.
7.) Why would you NOT want to use fraction form for ordering fractions, decimals, and percents
from least to greatest or greatest to least? If you changed everything to fraction form, then you
would have to find common denominators for each number which could prove to be
challenging.
8.) Draw your conversion chart without looking. Look at the bottom of page 7 notes
9.) Explain why some students make the common mistake of saying 0.124… ( repeating) is greater
than 0.7. Some students think 0.124 repeating is bigger because it goes on forever and they say
0.7 does not . 0.7 is bigger because of the tenths place and you could add zeros after the 7
forever if you chose.
10.) Explain how you could make the argument that part of all decimals repeat? You can always add
as many zeros to the end of any decimal without changing its value
11.) Why do some fractions such as 2/3, look as though they don’t repeat when dividing numerator
by denominator on a calculator? The calculator rounds the last digit on the screen because it
runs out of space
12.) When ordering fractions, decimals, percents, and scientific notation from least to greatest,
many students put all numbers into decimal form. However, they often get confused when
putting scientific notation into decimal form (especially with positive exponents). What is
considered decimal form for a number in scientific notation form? When changing a number in
scientific notation form to standard form, it’s important to remember that standard form is
decimal form.
13.) Why is making a place value chart important when ordering fractions, decimals, percents, and
scientific notation? This helps minimize errors made when ordering
14.) What do some students forget to do with the repeating decimals in their place value charts?
When adding zeros when lining up place values, be sure not to add zeros to repeating decimals,
you need to add whatever repeats…. See page 9 examples from your notes.
15.) How was the division symbol created? The division symbol represents a fraction… numerator
divided by denominator.
16.) Explain why Mr. Kurko doesn’t like using “alligator” when explaining less than or greater than
symbols. What is a better way? When using alligator students can’t tell which symbol is which
when they stand alone. Read a symbol like a book from left to right. If the small part is on the
left, this is ‘’less than’’. If the big part of the symbol is on the left, this is ‘’greater than’’.
17.) Sally had the fraction 5/12. She needed to convert it to a decimal by dividing without a
calculator. When she did this, she got 2.4. What did Sally do wrong and how should she have
discovered she was wrong right away? Sally divided her denominator by numerator. She should
recognize this right away because her answer should be less than 1.
18.) Divide the following fractions to get decimals using long division. (Go to the thousandths place)
3/7
8/9
7/12
**** To quickly check my answers, I know that none of the answers are greater than 1….Why
all numerators are less than the denominators
**** I also know that 3/7 should be less than 0.5 or 50%, 8/9 should be greater than 0.5 or 50%
and 7/12 should be greater than 0.5 or 50%. How do I know this? ...by looking at the fractions
and determining if they are less or more than half