Www.mathsrevision.com Created by Mr. Lafferty @ Scientific Notation Using the calculator and...
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Transcript of Www.mathsrevision.com Created by Mr. Lafferty @ Scientific Notation Using the calculator and...
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Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Scientific Scientific NotationNotation
ww
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Calculator
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Using the calculator for fractions
Simplifying Ratios
Ratio & Proportional Division
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Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Starter QuestionsStarter Questionsw
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S3.3
1. Write in scientifi c notation
(a) 2300 (b) 0.00534 (c) 569200 (d) 0.05060
2. True or f alse
5 5 1
6 12 2
3. Find the length of x
10cm
8cm
x cm
Calculator
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Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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1.1. To be able to use the To be able to use the calculator to calculate calculator to calculate values using scientific values using scientific notation.notation.
1. To show how to do calculation using scientific notation on the calculator.
Scientific Notation
S3.3 Calculator
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Using the calculator
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S3.3
We can use scientific notation on the calculator.Depending on your calculator you will use one of thefollowing buttons.
xy 10x EXP EE(you may have to use the shift button)
Enter the 5.4x103 into your calculatorCalculator Keys
5 4 xy0 3
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Using the calculator
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S3.3
xy 10x EXP EE(you may have to use the shift button)
Example: 6.25x10-7
Calculator Keys
6 2 xy0 -
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Example: 8.31x1011
Calculator Keys
75
8 3 xy0 1 11
Not the subtraction
button
Using the calculator
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S3.3
Calculate: 4 x 106 ÷ 8 x 106
It is good practice to put each value in brackets
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected] 66
4 xy0 6
(
(
xy0
)
68 )
exe
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Now try Ex 7.1 and Ex 7.2
Ch 1 (page 10)
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Using the calculator
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Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Starter QuestionsStarter Questionsw
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S3.3
3 -4
1. Write in scientifi c notation
(a) 4.5 x 2.3x10 (b) 0.053 x 3.4x10
2. True or f alse
5 5 1
6 3 3
3. Find the length of y
y cm
5cm
12 cm
Calculator
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Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
ww
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1.1. To be able to use the To be able to use the calculator to calculate calculator to calculate fractions.fractions.
1. To show how to do calculation using fractions on the calculator.
S3.3 Fractions
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Using the calculator
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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1010
Using the calculator
Reminder on fractions
A fraction has a numerator and denominator
The value of a fraction can be calculated bydividing the numerator by the denominator
A proper fraction has a value of less than 1
An improper fraction is of the form bab
a
A mixed number contains whole number and fractions
75.000.34
4
3
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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1111
Using the calculator
We can use the calculator when working with fractions
The fraction button is :
cba
Example 1: Express as a decimal 4
3
3 4cba 0.75
Fractions
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Using the calculator
Example 2: Express as a decimal 10
5
5 10cba 0.51┌2 c
ba
Example 3: Express as a mixed number 4
7
7 4cba 1┌3 ┌4
Fractions
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Using the calculator
Example 4: Express as a improper fraction3
24
4 2cba 14┌3c
ba3 2ndcba
Example 5: Add3
2
5
34
4 3cba
5┌4┌ 15
cba5c
ba 2 3 =
Fractions
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Now try Ex 8.1 and Ex 8.2
Ch 1 (page 13)
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Using the calculatorFractions
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Starter QuestionsStarter Questionsw
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(a) 123 (b) 202 (c) 0.09
1. Explain why x=4 when 3x + 5 = 17
2. True or f alse 20% of 220 = 44
3. How many signifi cant numbers
4. Car depreciates by 20% in its
fi rst year. I f it was bought new
f or £ 10 000. How much is it worth now.
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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1.1. Understand the term ratio. Understand the term ratio. ..
1. To understand what a ratio is and explain how we can sometimes simplify them.
RatiosRatios
2.2. Calculate and simplify Calculate and simplify basic ratios.basic ratios.
What is a ratio ?
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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RatiosRatios
Ratios can be used to compare different quantitiesRatios can be used to compare different quantities
What is a ratio ?
Example : There are 2 triangles and 3 rectangles.
The ratio of triangles to rectangles is said to be 2 : 3
Note: The ratio of rectangles to triangles is said to be 3 : 2
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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RatiosRatios
Simplifying a ratio is like simplifying fractionsSimplifying a ratio is like simplifying fractions
Simplifying a ratio ?
Fraction :÷2
÷2
6 6 3= =
8 8 4
Ratio : ÷2 ÷26 : 8 = 6 : 8 = 3 : 4
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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RatiosRatios
Sometimes we need to multiply to simplifySometimes we need to multiply to simplify
Simplifying a ratio ?
Ratio :1 : 5 =
31
×3 : 5×3 = 3
1 : 15
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RatiosRatios
When working with ratios, When working with ratios, the two units the two units MUSTMUST be the same be the same
Simplifying a ratio ?
Ratio :1 hour : 40 minutes
4
= 15 minutes : 40 minutes
= 3 minutes : 8 minutes
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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RatiosRatios
By first multiplying by ten to get rid of the decimalssimplifying the following ratios:
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Simplifying a ratio ?
(a) 2.2 : 3.3 22 : 33 2 : 3
(b) 1.6 : 9.6 16 : 96 1 : 6
(c) 0.5 : 100 5 : 1000 1 : 200
(d) 8.5 : 9.5 85 : 95 17 : 19
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RatiosRatios
By eliminating the fractions simplify the ratios.
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Simplifying a ratio ?
2 : 3
Multiply each side by 35 5 : 21
Multiply each side by 4
8 : 21
4
31:
3
2)(
5
3:7
1)(
4
3:2
1)(
c
b
a
Multiply each side by 12
Now try Ex 9.1Ch1 (page 16)
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RatiosRatiosSimplifying Ratios
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Starter QuestionsStarter Questionsw
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5 1 322 4 4
2. Calculate the area of the shape.
4. True or f alse
(a) 0.853 (b) 0.356 (c) 1.995
1. 6x + 5 = 59
3. Round to 2 decimal places.
9
8
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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1. Explain how to work out Ratio & Proportional division by using shares.
1. Work out the number of shares for a ratio.
RatiosRatiosRatio & Proportional Division
2. Solve problems using shares.
3. Show appropriate working.
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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RatiosRatios
Example : Bill and Ben share a raffle win of £400 in the ratio 3:5. How much does each get ?
Ratio & Proportional Division
Step 1 : Since the ratio is 3:5, there are :
3+5 = 8 shares
Step 2 : Each share is worth : 50
8 400
Step 3 : Bill gets 3 x 50 = £150
Ben gets 5 x 50 = £250Check !150 + 250 = 400
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RatiosRatios
Example : Ryan and Ross share 24 cakes in the ratio3:1. How many cakes does each get ?
Ratio & Proportional Division
Step 1 : Since the ratio is 3:1, there are :
3+1 = 4 shares
Step 2 : Each share is worth : 6
4 24
Step 3 : Ryan gets 3 x 6 = 18
Ross gets 1 x 6 = 6Check !18 + 6
= 24Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty
Now try Ex 9.2Ch1 (page 16)
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RatiosRatiosRatio & Proportional Division
Wednesday, April 19, 2023Wednesday, April 19, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]