Estimating decimals

In this lesson, we will learn:

• How to use number lines to help estimate decimal values (to the closest whole number or closest tenth)
• How to round decimal numbers to the nearest whole number, or the nearest tenth

Notes:

• To estimate means to roughly guess the value (or a rough calculation)
• For estimating decimals, have less decimal place values in your number
• Rounding is one strategy for estimation; by making numbers less exact (less precise), they become simpler or easier to do math with
• We use the symbol $\approx$ meaning "about equal to" for estimation and rounding
• Ex. 39 is about equal to the even number 40; 39 $\approx$ 40


• We can use number lines to help estimate decimal values
• Find the closest distance to the nearest whole number OR the nearest tenth
• Ex. rounding 0.3 to the nearest whole number, is it closer to 0 or 1?

• 0.3 is closer to 0 than it is to 1. Therefore, 0.3 $\approx$ 0

• Ex. rounding 0.66 to the nearest tenth, is it closer to 0.6 or 0.7?

• 0.66 is closer to 7 than it is to 6. Therefore, 0.66 $\approx$ 0.7

• The steps for rounding numbers:
1. Look at the place value you are rounding to ("target").
   $\quad \, \longrightarrow \;$ start writing a new rounded number, where:
   $\quad \, \longrightarrow \;$ any smaller place values (to the right) can be changed to zero
   $\quad \, \longrightarrow \;$ any bigger place values (to the left) can be kept
2. Look at the place value to the right of where you are rounding to.
   1. if the digit is $\geq 5$, round up (increase the target by 1)
   2. if the digit is < 5, round down (keep the target the same)
3. Any trailing zeroes in decimals can be removed (i.e. 0.50 = 0.5; 2.0 = 2)

• When your target digit is 9, if you round up then you will regroup to the next place value up.
• Ex. Rounding 0.97 to nearest tenth $\, \longrightarrow \,$ round up from 0.9 to 1.0; 0.97 $\approx$ 1.0