Math 58 Supplement
Rounding and Units
1
Rounding
• First, we need to decide what place value you want to round
to; this is usually given
• For the following number: 1234.567
• 1 is in the thousands place
• 2 is in the hundreds place
• 3 is in the tens place
• 4 is in the ones place
• 5 is in the tenths place
• 6 is in the hundredths place
• 7 is in the thousandths place
2
Place Value Examples
• A number in the tens place has the value times 10:
30 has the value 3 x 10
• A number in the hundredths place has the value times
0.004 has the value 4 x
1
1000
1
1000
3
Rounding
• Given the place to which we need to round, we need to look
at the value to the right of that place, the smaller place
• For example, if we want to round 3.456 to the hundredths
place, we need to look at the value in the thousandths place
• If the number to the right is 5 or above, we increase our value
by one
• If the number to the right is less than 5, we leave the value
as is
• Round to the hundredths place:
3.456 becomes 3.46
3.452 becomes 3.45
4
Examples
Round 3,956,813.2357 to the nearest
• Hundreds
• Tenths
• Millions
• Thousandths
• Ones
5
Solutions
Round 3,956,813.2357 to the nearest
• Hundreds: 3,956,800
• Tenths: 3,956,813.24
• Millions: 4,000,000
• Thousandths: 3,956,813.236
• Ones: 3,956,813
6
Units
• We measure almost everything that exists in the real world
• Unfortunately, we use different units to measure small things
than we do large things
– We wouldn’t measure the length of an ant in miles
– We wouldn’t measure the radius of the earth in inches
• Therefore, we need to be able to convert units so that we can
compare our measurements
7
How to Convert
• Take two quantities that are equal and make a fraction out
of them
1 foot = 12 inches so
1 feet
12 inches
=
12 inches
1 feet
=1
• Once we have this fraction, we can convert from feet to
inches: The key is that the units need to “cancel”
• Convert 3 feet to inches:
3 feet
12 inches
1 feet
=
3 𝑓𝑒𝑒𝑡
1 𝑓𝑒𝑒𝑡
12 𝑖𝑛𝑐ℎ𝑒𝑠 =
3 𝑓𝑒𝑒𝑡
1 𝑓𝑒𝑒𝑡
12 𝑖𝑛𝑐ℎ𝑒𝑠
= 36 inches
8
Another Example
• If there are 4 cups in a quart, how many quarts are 15 cups?
• Create a fraction:
4 𝑐𝑢𝑝
1 𝑞𝑢𝑎𝑟𝑡
=
1 𝑞𝑢𝑎𝑟𝑡
4 𝑐𝑢𝑝
=1
• Then, convert:
15 cup
1 𝑞𝑢𝑎𝑟𝑡
4 𝑐𝑢𝑝
=
15 𝑐𝑢𝑝
4 𝑐𝑢𝑝
quart =
15
4
quarts or 3.75 quarts
9
Examples
Convert the following:
• 10.5 liters to cups, if 1 liter = 4.2 cups
• 25 oz to pounds if 1 pound = 16 oz
• 500 yards to miles if 1 mile is 5280 feet
10
Solutions
• 10.5 liters to cups, if 1 liter = 4.2 cups
10.5 (4.2/1) = 44.1 cups
• 25 oz to pounds if 1 pound = 16 oz
25/16 = 1.5625 pounds
• 500 yards to miles if 1 mile is 5280 feet
1 yard is 3 feet
500 yd (3 ft/yd) ( 1mi / 5280 ft) ~ 0.28 mi
11