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Maths Year 9 > Numbers > Flashcards

Numbers Flashcards

1
Q

What is place value, and how does it work in a number like 4.58?

A

Place value determines the value of a digit based on its position in the number. In 4.58, 4 is in the units place, 5 is in the tenths place, and 8 is in the hundredths place.

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2
Q

What is the value of the digit 7 in the number 0.0784?

A

7/100 or 0.07

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3
Q

What does it mean to round a number?

A

Rounding a number means adjusting it to the nearest specified place value (e.g., nearest whole number, decimal place, or significant figure) based on the value of the digits.

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4
Q

Round 456.789 to two decimal places.

A

456.79

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5
Q

What is an improper fraction, and how does it differ from a mixed number?

A

An improper fraction has a numerator larger than the denominator (e.g., 7/4), while a mixed number combines a whole number and a fraction (e.g., 1 3/4).

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6
Q

Convert the mixed number 3 1/2 into an improper fraction.

A

7/2

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7
Q

What does it mean to simplify a fraction?

A

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1.

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8
Q

Simplify the fraction 18/24.

A

3/4

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9
Q

How do you convert a decimal into a fraction?

A

To convert a decimal into a fraction, write it as a fraction with a denominator based on its place value (e.g., 0.75 = 75/100 = 3/4) and simplify.

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10
Q

Convert 0.375 into a fraction.

A

3/8

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11
Q

What does it mean for a decimal to be recurring?

A

A recurring decimal has one or more repeating digits or sequences of digits after the decimal point, such as 0.333… (repeating 3).

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12
Q

Round 5.6789 to three decimal places.

A

5.679

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13
Q

What is a percentage, and how is it related to fractions and decimals?

A

A percentage represents a number as a fraction of 100. It can be converted to a fraction (e.g., 25% = 25/100 = 1/4) or a decimal (e.g., 25% = 0.25).

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14
Q

What is 25% of £60?

A

£15

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15
Q

What does it mean to calculate percentage change?

A

Percentage change measures how much a quantity has increased or decreased relative to its original value, calculated as (change/original value) × 100%.

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16
Q

If the original price is £80 and the price after discount is £60, what is the percentage discount?

A

0.25

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17
Q

What is a power (or exponent), and how does it work in a number like 2^3?

A

A power represents how many times a number is multiplied by itself. In 2^3, 2 is multiplied by itself three times (2 × 2 × 2 = 8).

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18
Q

What is 4^3?

A

64

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19
Q

What is a square root, and how is it related to squaring a number?

A

A square root is a value that, when multiplied by itself, gives the original number (e.g., √16 = 4, because 4 × 4 = 16).

20
Q

Simplify the expression 16^(1/2).

A

4

21
Q

What is standard form, and why is it useful?

A

Standard form is a way of writing very large or very small numbers as a product of a number between 1 and 10 and a power of 10 (e.g., 4,500 = 4.5 × 10^3).

22
Q

Write 0.00045 in standard form.

A

4.5 × 10^(-4)

23
Q

What does it mean to round a number to a certain number of significant figures?

A

Rounding to significant figures involves adjusting a number to reflect only its most important digits, based on the precision required (e.g., 5678 rounded to 2 significant figures is 5700).

24
Q

Round 5678 to 2 significant figures.

A

5700

25
Q

What is a ratio, and how does it differ from a fraction?

A

A ratio compares two quantities (e.g., 3:4) showing how much of one there is compared to the other. Unlike fractions, ratios can compare more than two quantities.

26
Q

Simplify the ratio 12:16.

A

3:4

27
Q

What is direct proportion?

A

Direct proportion means that two quantities increase or decrease at the same rate, such that their ratio remains constant.

28
Q

If 5 apples cost £2, how much do 8 apples cost?

A

£3.20

29
Q

How do you compare two fractions to determine which is larger?

A

To compare fractions, convert them to a common denominator or decimal form, then compare their values.

30
Q

Which is larger: 3/4 or 0.75?

A

They are equal.

31
Q

What does the inequality symbol ‘<’ represent?

A

The symbol ‘<’ means ‘less than’ and is used to show that one number is smaller than another.

32
Q

Write the inequality that represents the relationship: -5 and -3.

A

-5 < -3

33
Q

What is a prime number?

A

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself (e.g., 2, 3, 5).

34
Q

List the prime factors of 60.

A

2, 3, 5

35
Q

What is the highest common factor (HCF)?

A

The HCF is the largest number that divides exactly into two or more numbers (e.g., the HCF of 24 and 36 is 12).

36
Q

What is the HCF of 24 and 36?

A

12

37
Q

What is estimation, and why is it useful?

A

Estimation involves finding an approximate value that is close enough to the right answer for practical purposes, often by rounding numbers.

38
Q

Estimate the value of 4.7 × 8.2 by rounding each number to the nearest whole number.

A

Approximately 40 (since 5 × 8 = 40)

39
Q

What are bounds of accuracy?

A

Bounds of accuracy refer to the range within which the true value of a rounded number lies (e.g., 7.5 rounded to the nearest tenth is between 7.45 and 7.55).

40
Q

If a measurement is given as 7.5 cm to the nearest tenth, between what two values could the actual measurement lie?

A

Between 7.45 cm and 7.55 cm

41
Q

What is the order of operations (BIDMAS/BODMAS)?

A

BIDMAS/BODMAS stands for Brackets, Indices (powers), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). It dictates the correct sequence to follow when performing calculations with multiple operations.

42
Q

What is 45 × 7 + 6 ÷ 3?

A

317 (following BIDMAS/BODMAS rules).

43
Q

What happens when you add or subtract negative numbers?

A

Adding a negative number is the same as subtracting, and subtracting a negative number is the same as adding. For example, 5 + (-3) = 2, and 5 - (-3) = 8.

44
Q

What is -7 + 3?

A

-4

45
Q

How can you use a calculator to perform operations with fractions?

A

Most calculators allow you to enter fractions directly using a fraction key, or you can convert fractions to decimals to perform operations.

46
Q

Use a calculator to find the value of 3.6 ÷ 0.12.

A

30

Maths Year 9 (3 decks)

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