Math Review
Chemistry
Rounding:
9876540.987654321
Millionths
Hundred Thousdanths
Ten Thousandths
Thousandths
Hundredths
Tenths
Ones
Tens
Hundreds
Thousands
Ten Thousands
Hundred Thousands
Millions
When asked to round to a place value, the number should END at that place value. To do this
you look at the next number. If it is LESS THAN 5, just drop all the numbers after the place
value you want. If it is 5 OR MORE you still drop all the numbers past your place value, but you
also must round the last number that you are keeping up 1 value.
For example:
Example 1:
Round to the nearest thousandth.
1.023548643
This is less
than 5 so the
6 stays the
same.
Answer: 1600
Example 3:
Round to the nearest ones.
0.81235
Must stop
here!
Answer: 1.024
1623.657
Must stop
here!
Must stop
here!
This is 5 or
more so 3
rounds up to a
4.
Example 2:
Round to the nearest hundred.
This is 5 or
more so 0
rounds up to a
1.
Answer: 1
Now you try!
1) .1325 to thousandths
5) 6.6666 to thousandths
9) .0091 to hundredths
2) .0091 to thousandths
6) 40.61884 to thousandths
10) .3333 to hundredths
3) .0196 to thousandths
7) 1.99999 to thousandths
11) 5.567 to hundredths
4) 5.1234 to thousandths
8) .1325 to hundredths
12) 48.001 to hundredths
Scientific Notation:
We use scientific notation to make REALLY BIG numbers or REALLY SMALL numbers easier to
work with. A number in scientific notation has a single number between 1-9 to the left of the
decimal and then is multiplied by 10 to the power of how far we moved the decimal.
Example 1:
Example 2:
602200000000000000000000.
0.00000000000000000005684
23x to the left
Example 3:
20x to the right
Answer: 6.022 x 1023
8
3.0 x 10
Answer: 5.684 x 10-20
Example 4:
Move 34x to the left
Move 8x to the right
Answer: 300000000
6.63 x 10-34
Answer: 0.000000000000000000000000000000000663
***Notice that when the exponent is negative the value of the actual number is between zero
and one, but when the exponent is positive the value of the actual number is greater than
one.***
Now you try!
Write the following numbers in scientific notation:
1. 1001
2. 53
3. 6,926,300,000
4. -392
6. 0.13592
7. -0.0038
8. 0.00000013
9. -0.567
5. 0.00361
Convert the following from scientific notation to decimal:
1. 1.92 x 103
2. 3.051x101
3. -4.29 x 102
4. 6.251 x 109
6. 1.03 x 10-2
7. 8.862 x 10-1
8. 9.512 x 10-8
9. -6.5 x 10-3
5. 8.317 x 106
10. 3.159 x 102