Rounding Numbers – Part 1 Slideshow 1, Mathematics, Mr Richard Sasaki

Objectives Understand the concept of rounding Understand the meaning of decimal places, truncation and rounding up Be able to round numbers up and down

Introduction What’s an easy sounding number close to 9.972? 10 Solving 10×3.6 sounds much easier than 9.972×3.6. Their answers are very close. 10 × 3.6= 36 There is an 0.1008 inaccuracy. 9.972 × 3.6 = 35.8992 Finding approximate values like this is fine when we don’t need to be exact. However, there are rules. First, let’s look at decimal places.

Decimal Places Look at the decimal number below. 24.9763 It has decimal places. 4 1. Let’s round it to 3 decimal places. 24.976 24.9763 is between 24.976 and 24.977. Which is closer? 2. Let’s round it to 2 decimal places. 24.98 24.9763 is between 24.97 and 24.98. Which is closer? We round up and down to whatever is closest.

Special Cases Example Round 7.5 to the nearest integer. 7.5 is equal distance from 7 and 8. Either is okay but 8 is more common. Note: Different teachers may treat this situation differently. Example Round 6.99 to 1 decimal place. We should write 7.0 to show it is to 1 decimal place but 7 is okay.

3 4.015 3.28 4.02 3.3 4.0 3 57.3159 57.32 57 0.7924 0.79 1 43.2948 43.29 43 6.2364 6.24 6 284.3349 284.33 284 7.2949 7.29 7 4.0001 4.00 4 1.9997 2.00 2

Tricky Question The number shown was rounded to 2 decimal places. 24.55 Does this mean that the number must be 24.6 rounded to 1 decimal place? No…it doesn’t. If the number is 24.5 rounded to 1 decimal place, what could it have been? 24.5 1 d.p 24.6 1 d.p 24.548 2 d.p 24.55 Rounding twice (or more) can be bad! It creates inaccuracy.

Truncation Some units can’t be split up, so we truncate. Truncation means to . We cut off the part we don’t need. round down When do we do this in real life? We truncate with money. ¥89÷10= . ¥8 You can’t give someone ¥8.9 and you can’t make money from nothing. Note: It is useful to keep decimal amounts of money when calculating further. When ordering items in bulk, you may see decimal amounts in magazines.

Rounding Up We need to be able to identify whether we need to round up or truncate. How many 1 litre bottles do we need to hold 3.1 litres? 4 bottles How many 1 litre bottles would 3.1 litres fill? 3 bottles

Answers 3 notes 4 portions 8 𝑘𝑔 5 sweets 5 bags 4 cartons 2 years 3 Yen 20 files 178 Yen