Grade 5: Review
Topics:
1) Rounding Decimals
2) Comparing Fractions and Decimals
3) Even, Odd, Composite, and Prime Numbers
Introduction to Digits
The following images shows all the different digits from thousands to ten thousandths. The digits are centered about the decimal point but remember when counting from the right you start with tenths.
REMEMBER: Starting at the right of the decimal point the first digit is tenths, and an easy way to remember is that you add -ths to the digits when you go to the right of the decimal oneths sounds a bit weird to say.
Rounding Decimals
Rounding Decimals
for 5 and above round up
Example 1.7677 ~ 1.768
for below 5 round down
Example 1.8421 ~ 1.842
Rounding Decimals Practice
Round the Following to the nearest:
1) 1.676 to the nearest tenth
2) 0.578 to the nearest hundredth
3) 19.35511 to the nearest thousandth
4) 6.992232 to the nearest hundred thousandth
5) 5.53411 to the nearest ten
Answers:
1) 1.7
2) 0.58
3) 19.355
4) 6.99223
5) 10
Rounding Decimals Practice Explanation
1) 1.676 to the nearest tenth
The first step is to identify the tenths digit:
1.676
Then look to the number to the right of the tenths digit
If it is above 5 we round the tenths digit up
If it is below a 5 we leave the tenths digit unchanged
1.676 <--------- because 7>5 we will round up
Answer: 1.7
2) 0.578 to the nearest hundredth
The first step is to identify the hundredths digit:
0.578
Then look to the number to the right of the hundredths digit
If it is above 5 we round the tenths digit up
If it is below a 5 we leave the tenths digit unchanged
0.578<--------- because 8>5 we will round up
Answer: 0.58
3) 19.35511 to the nearest thousandth
The first step is to identify the thousandth digit:
19.35511
Then look to the number to the right of the thousandth digit
If it is above 5 we round the tenths digit up
If it is below a 5 we leave the tenths digit unchanged
19.35511<--------- because 1<5 we will not round up
Answer: 19.355
4) 6.992232 to the nearest hundred thousandth
The first step is to identify the hundred thousandth digit:
6.992232
Then look to the number to the right of the tenths digit
If it is above 5 we round the tenths digit up
If it is below a 5 we leave the tenths digit unchanged
6.992232<--------- because 2<5 we will not round up
Answer: 6.99223
5) 5.53411 to the nearest ten
The first step is to identify the ten digit:
_5.53411
Then look to the number to the right of the tens digit
If it is above 5 we round the tenths digit up
If it is below a 5 we leave the tenths digit unchanged
_5.53411<--------- because 5=5 we will round up
Answer: 10
Comparing Fractions and Decimals
In order to compare fractions and decimals you have to make them easily comparable:
You can convert simple fractions into decimals
3/4 --> 0.75
You can convert simple decimals into fractions
1.75 --> 7/4
You can convert simple fractions into mixed fractions and compare the non fractional part
19/2 --> 9 1/2
You can approximate the decimal form of more complex fractions using long division
3/7 --> 0.429
You can easily tell negative numbers will be less than positive numbers
-102.233423 --> OH NO what a big scary negative number
Example: Order 1.72, 4/5, -1/5, 7/4 from least to greatest
Steps:
1) -1/5 is the lowest because it is the only negative
2) 4/5 = 0.8 and 7/4 = 1.75
3) 7/4>1.72
Answer: -1/5, 4/5, 1.72, 7/4
Comparing Fractions and Decimals Practice
Order the Following from least to greatest:
1) 3/8, 1 5/8, 75%, 0.33, -1/8
2) 2, 3/4, 8/12, 3 5/8, -12/16
3) 1.6, 6/4, 9/12, 3 5/8, -12/16
Hint: Try converting fractions into decimals and vice-versa(Try not to use a calculator unless you are stuck)
Answers
1) -1/8 < 0.33 < 3/8 < 75% < 1 5/8
2) -12/16 < 8/12 < 3/4 < 2 < 3 5/8
3) -12/16 < 9/12 < 6/4 < 1.6 < 3 5/8
More Practice:Real Numbers
Comparing Fractions and Decimals Practice Explanation
1) 3/8, 1 5/8, 75%, 0.33, -1/8
1) We can see that -1/8 will be the lowest number
2) We can see that 1 will be the greatest because the rest are decimals and fractions below 1
3) We can see that:
3/8 < 5/8
4) Now the hardest part is to compare the following:
3/8 and 0.33
3/8 = 0.375 <-- by long division
0.375 > 0.33
5) Now to compare the following:
5/8 and 75%
5/8 = 0.625
75% = 0.75
0.75>0.625
Answer: -1/8<0.33<3/8<5/8<75%<1
Even, Odd, Prime, and Composite Numbers
Even: Divisible by 2
Example: 92, 4, 56
Odd: Not divisible by 2
Example: 97, 121, 1
Prime: Only divisible by 1 and the number itself:
Example: 13, 29, 31
Composite: Divisible by other whole number(not prime)
Example: 6, 8, 10
Exceptions: Numbers that are neither prime nor composite
Example: 0 and 1
Even, Odd, Prime, and Composite Numbers Practice
Categorize the Following(2 terms each):
1) 2
2) 0
3) 1
4) 5
5) 9
6) 192
7) 23
8) Final Boss: 1231231231321487953457230495273894523123123123122
Answers:
even, prime
even (neither prime nor composite)
odd (neither prime nor composite)
odd, prime
odd, composite
even, composite
odd, prime
even, composite