M S1 Measurement 1 Accuracy PP

MUPCMaths and Statistics 1 : 

MUPCMaths and Statistics 1 Measurement 1 Standard Form

Scientific Notation : 

Scientific Notation Standard form / Scientific Notation Change back to normal form

Slide 3: 

Learning Objective Success Criteria To understand and use the quick method to put large or small numbers into scientific notation. To show a very quick way of putting a large or small number into scientific notation. Scientific Notation

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Standard Form and Very large numbers! How far? 92 000 000 miles

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70 years = 2 200 000 000 seconds! Very large numbers! SPAT!

Slide 6: 

Dinosaurs roamed the earth 228 000 000 years ago Very large numbers!

Slide 7: 

Standard Form 100 = 10 x 10 1 000 = 10 x 10 x 10 100 000 = 10 x 10 x 10 x 10 x 10 10 000 = 10 x 10 x 10 x 10 1 000 000 = 10 x 10 x 10 x 10 x 10 x 10 10

Slide 8: 

Standard Form 200 = 2 x 100 4 000 = 4 x 1000 500 000 = 5 x 100 000 70 000 = 7 x 10 000 3 000 000 = 3 x 1 000 000

Slide 9: 

Standard Form Exercise 1 2 000 (2) 20 000 (3) 500 (4) 800 000 (5) 9 000 000 = 5 x 100 = 8 x 100 000 = 2 x 10 000 = 9 x 1 000 000 = 2 x 1000

Slide 10: 

A short cut 8 000 000 . . Move the point to get a number between 1 and 10 www.mathsrevision.com S3.3 a x 10n where 1 ≤ a < 10 n is positive or negative

Slide 11: 

92 000 000 . . Move the point to get a number between 1 and 10 www.mathsrevision.com A short cut S3.3

Slide 12: 

2 200 000 000 . . Move the point to get a number between 1 and 10 Happy Birthday: Seconds old! A short cut S3.3

Slide 13: 

228 000 000 . . Move the point to get a number between 1 and 10 www.mathsrevision.com A short cut S3.3

Slide 14: 

www.mathsrevision.com Standard Form (1) 30 000 (2) 700 000 (3) 5 300 (4) 470 000 (5) 9 500 000 (6) 18 300 000 (7) 329 000 (8) 2 560 000 (9) 12 000 000 000 (10) 9 990 000 S3.3

Scientific Notation : 

Scientific Notation www.mathsrevision.com Learning Intention Success Criteria Know how to expand large numbers in scientific notation to number format. To understand how to change large numbers from Scientific Notation to number form. S3.3

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=86 000 000 8.6 0000000 . Hint: Add 7 zeros, although you probably won’t need them all. www.mathsrevision.com Changing back S3.3

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www.mathsrevision.com =346 000 3.46 00000 . Hint: Add 5 zeros, although you probably won’t need them all. Changing back S3.3

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www.mathsrevision.com Changing back (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) = 600 000 = 8 000 = 650 000 = 120 000 000 = 3 710 000 = 33 000 = 7 910 000 = 55 500 000 = 10 500 = 3 033 000 000 S3.3

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Very small numbers! How wide is an atom? 0.000 000 000 1 metres wide! www.mathsrevision.com S3.3

Slide 20: 

0.000 000 000 1 . Move the point to get a number between 1 and 10 www.mathsrevision.com Standard Form for small numbers S3.3

Slide 21: 

0.000 000 76 . Move the point to get a number between 1 and 10 www.mathsrevision.com Standard Form for small numbers S3.3

Slide 22: 

Standard Form for small numbers 0.000 001 93 . Move the point to get a number between 1 and 10 www.mathsrevision.com S3.3

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Standard Form for small numbers www.mathsrevision.com (1) 0. 000 3 (2) 0.000 07 (3) 0.000 45 (4) 0.003 4 (5) 0. 000 724 (6) 0.000 000 494 (7) 0.000 095 (8) 0.000 000 098 (9) 0.000 1 03 (10) 0.000 000 000 66 S3.3

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= 0.002 2 000 . Hint: Add 3 zeros to the left of the number. . www.mathsrevision.com Changing back small numbers S3.3

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= 0.000 086 8.6 00000 . Hint: Add 5 zeros to the left of the number. www.mathsrevision.com Changing back small numbers S3.3

Slide 26: 

Changing back small numbers = 0.000 00516 5.16 000000 . Hint: Add 6 zeros to the left of the number. www.mathsrevision.com S3.3

Slide 27: 

www.mathsrevision.com (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) = 0.000 5 = 0.000 09 = 0.005 8 = 0.000 000 62 = 0.000 006 45 = 0.000 000 53 = 0.000 009 17 = 0.002 12 = 0.000 020 3 = 0.000 000 006 032 Changing back small numbers S3.3

Slide 28: 

Why do we need to round numbers? You may see it reported that a TV program had 23 million viewers. This is not actually true because some of those viewers fell asleep half way through the program and some people lied about watching the program. The true number of viewers was somewhere between 22½ million and 23½ million and the published figure was rounded to the nearest million.

Slide 29: 

When you have to round a number, you are usually told how to round it. It's simplest when you're told how many "places" to round to, but you should also know how to round to a named "place", such as "to the nearest thousand" or "to the hundred". You may also need to know how to round to a certain number of significant figures. Rounding Numbers

Slide 30: 

Similarly if you used your calculator to find the square root of 1000, you would get something like: √1000 = 31.622776601683793319988935444327 The most important digits are the 3, 1 and 6 at the beginning. The least important digits are the 3, 2 and 7 at the end. It is bad practice to write down all the digits that the calculator shows so we choose only to write down a few of the most important ones.

Slide 31: 

Rounding to the nearest ten and the nearest Looking at the number above, it should be seen that, to the nearest ten, the square root of 1000 is 30. The above number is between 30 and 40 and it is nearer to 30. This is an example of rounding down. √1000 = 31.622776601683793319988935444327

Slide 32: 

To the nearest whole number, the square root of 1000 is actually 32 because the number given above is closer to 32 than to 31. This is an example of rounding up. Rounding to the nearest whole number √1000 = 31.622776601683793319988935444327

Slide 33: 

Round up or round down? To decide whether to round up or down we look at the digit next to those that we plan to write down. When we rounded to the nearest ten, this digit was the 1 in the units place. √1000 = 31.6227766016837..................

Slide 34: 

When we rounded to the nearest whole number, this digit was the first digit after the decimal point, the 6. If this digit is less than 5, we round down, if it is equal to or more than 5, we round up. This rule is used whether we are rounding to the nearest million or rounding to 2 decimal places √1000 = 31.6227766016837..................

Round this number to the nearestten thousand. : 

Round this number to the nearestten thousand. Find your digit. 3 6 8,9 7 1 Circle the digit in the ten thousands place.

Round this number to the nearestten thousand. : 

Round this number to the nearestten thousand. Look right next door. 3 6 8,9 7 1 Draw an arrow to the right of the number.

Round this number to the nearestten thousand. : 

Round this number to the nearestten thousand. The digit next door is 5 or more 3 6 8,9 7 1 Add 1 to the 6 and all the numbers to the right of the 7 become 0’s. 3 7 0,0 0 0

The Answer : 

The Answer 368,971 rounded to the nearest ten thousand is 3 7 0,0 0 0

Round this number to the nearestthousand. : 

Round this number to the nearestthousand. Find your digit. 3 5, 3 2 7 Circle the digit in the thousands place. units Tens of thousands thousands hundreds tens

Round this number to the nearestthousand. : 

Round this number to the nearestthousand. Look right next door. 3 5, 3 2 7 Draw an arrow to the right of the number.

Round this number to the nearestthousand. : 

Round this number to the nearestthousand. 4 or less, just ignore. 3 5, 3 2 7 Since 3 is less than 4 we do not change the 5.

Round this number to the nearestthousand. : 

Round this number to the nearestthousand. 4 or less, just ignore. 3 5, 0 0 0 Change the numbers to right of 5 to 0’s. 35,327 rounded to the nearest thousand is 3 5, 0 0 0

Round this number to the nearestdollar. : 

Round this number to the nearestdollar. Find your digit: $ 5. 8 7 Circle the digit where the dollars are. Look right next door. $ 5. 8 7 Draw an arrow to the right of the circled number. Since 8 is greater than 5 add 1 to the 5. $6.00 $5.87 rounded to the nearest dollar is

Slide 44: 

Rounding to a given number of decimal places

Slide 45: 

In general, you round to a given number of decimal places by looking at the digit one place to the right of the target place. If the digit is a five or greater, you round the target digit up by one. Otherwise, you leave the target as it is. Then you replace any digits to the right with zeroes (if they are to the left of the decimal point) or else you delete the digits (if they are past the decimal point).

Slide 46: 

Example 1 Pi = 3.14159265... Round pi to five decimal places. First, count out the five decimal places, and then look at the sixth place: 3.14159 | 265... Draw a little line separating the fifth place from the sixth place. This can be a handy way of "keeping your place", especially if you are dealing with lots of digits.

Slide 47: 

The line marks the target place. The first digit to the right of the target place is a 2. Since 2 is less than five, we won't round the 9 up. We leave the 9 as it is and delete the digits after the 9. Then pi, rounded to five places, is: 3.14159 (5dp) 3.14159 | 265...

Slide 48: 

Example 2 Pi = 3.14159265... Round pi to four decimal places. First, count out the four decimal places, and then look at the fifth place: 3.1415 9265.... Draw a little line separating the fourth place from the fifth place.

Slide 49: 

The line marks the target place. The first digit to the right of the target place is a 9. Since 9 is more than five, we must round the 5 up. (i.e. Add 1 to the digit 5) Then pi, rounded to four places, is: 3.1416 (4dp) 3.1415 9265....

Slide 50: 

Round pi to three places. Count off three decimal places, and look at the digit in the fourth place: 3.141 | 59265... The number in the fourth place is a 5 If the number after the target place is 5 or greater, you round up. In this case, the 1 becomes a 2, the 59265... part disappears, and pi, rounded to three decimal places, is: 3.142 (3dp)

Slide 51: 

Examples of Rounding numbers:

Slide 52: 

Examples of Rounding Decimals:

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Complete Question 1, page 3 Measurement 1: Accuracy Any work not completed during class must be completed for homework