Answer:i. The numbers of significant digits/ figures in the following numbers are:

a) 0.85 - 2 significant digits

b) 22.4 - 3 significant digits

c) 0.849 - 3 significant digits

d) 501.381 - 6 significant digits

e) 0.435 - 3 significant digits

f) 1.233 - 4 significant digits

g) 0.71 - 2 significant digits

h) 0.1473 - 4 significant digits

ii. Examples of terminating fractions:

1. 1/2 = 0.5

2. 3/4 = 0.75

3. 2/5 = 0.4

4. 5/8 = 0.625

5. 7/10 = 0.7

Examples of recurring fractions:

1. 1/3 = 0.333...

2. 2/7 = 0.285714285714...

3. 5/6 = 0.833333...

4. 4/9 = 0.444...

5. 7/11 = 0.636363...

Examples of non-terminating fractions:

1. 1/7 = 0.142857142857...

2. 3/5 = 0.6

3. 5/6 = 0.833333...

4. 4/9 = 0.444...

5. 2/3 = 0.666...

iii. Rounding off the following numbers up to 3, 4, and 5 significant figures:

a) 612737

  - 3 significant figures: 613000

  - 4 significant figures: 612700

  - 5 significant figures: 612740

c) 289.923

  - 3 significant figures: 290

  - 4 significant figures: 289.9

  - 5 significant figures: 289.92

e) 53.3728

  - 3 significant figures: 53.4

  - 4 significant figures: 53.37

  - 5 significant figures: 53.373

iv. Converting the following terminating fractions to decimals and rounding off to 3 significant digits:

a) 1/4 = 0.250

b) 18/29 = 0.621

c) 2/9 = 0.222

d) 7/8 = 0.875

e) 7/11 = 0.636

v. Converting the following non-terminating fractions to decimals and rounding off to 3 significant digits:

a) 1/3 = 0.333

b) 2/7 = 0.286

c) 5/6 = 0.833

d) 4/9 = 0.444

Step-by-step explanation:

i. The number of significant digits in the given numbers is

a) 0.85 - 2 significant digits b) 22.4 - 3 significant digits

c) 0.849 - 3 significant digits d) 501.381 - 6 significant digits

e) 0.435 - 3 significant digits f) 1.233 - 4 significant digits

g) 0.71 - 2 significant digits h) 0.1473 - 4 significant digits

ii. Examples of terminating fractions are 1/3, 2/5, etc.

Examples of recurring fractions are 0.999..., 0.8333...., etc.

Examples of non-terminating fractions are 0.11...., 0.5454..., etc.

iii. The given numbers are rounded off up to 3, 4, and 5 significant figures.

a) 612737:

Up to 3 significant figures = 613000

Up to 4 significant figures = 612700

Up to 5 significant figures = 612740

c) 289.923:

Up to 3 significant figures = 290

Up to 4 significant figures = 289.9

Up to 5 significant figures = 289.92

e) 53.3728:

Up to 3 significant figures = 53.4

Up to 4 significant figures = 53.37

Up to 5 significant figures = 53.373

iv. The given terminating fractions are converted to decimals.

a) 1/4 = 0.250 b) 3/5 = 0.600 c) 2/9 = 0.222 d) 5/6 = 0.833

e) 7/8 = 0.875 f) 7/11 = 0.636

v. The given non-terminating fractions are converted to decimals.

a) 1/3 = 0.333 b) 5/6 = 0.833 c) 2/7 = 0.285 d) 4/9 = 0.444

Given:

Some questions are given.

To Find:

The answer to the given questions.

Solution:

i. The significant digits are the non-zero digits and the digit 0 that has some value. It means if 0 is at the beginning of any number, it will not be considered.

The number of significant digits in the given numbers is

a) 0.85 - 2 significant digits b) 22.4 - 3 significant digits

c) 0.849 - 3 significant digits d) 501.381 - 6 significant digits

e) 0.435 - 3 significant digits f) 1.233 - 4 significant digits

g) 0.71 - 2 significant digits h) 0.1473 - 4 significant digits

ii. In terminating fractions, the decimals end at some point.

In recurring fractions, the decimals repeat a pattern for an indefinite time.

In non-terminating fractions, the decimals do not end.

Examples of terminating fractions are 1/3, 2/5, etc.

Examples of recurring fractions are 0.999..., 0.8333...., etc.

Examples of non-terminating fractions are 0.11...., 0.5454...

iii. The given numbers are rounded off up to 3, 4, and 5 significant figures.

a) 612737:

Up to 3 significant figures = 613000

Up to 4 significant figures = 612700

Up to 5 significant figures = 612740

c) 289.923:

Up to 3 significant figures = 290

Up to 4 significant figures = 289.9

Up to 5 significant figures = 289.92

e) 53.3728:

Up to 3 significant figures = 53.4

Up to 4 significant figures = 53.37

Up to 5 significant figures = 53.373

iv. In terminating fractions, the decimals end at some point.

The given terminating fractions are converted to decimals. They are rounded off to 3 significant digits.

a) 1/4 = 0.250

b) 3/5 = 0.600

c) 2/9 = 0.222

d) 5/6 = 0.833

e) 7/8 = 0.875

f) 7/11 = 0.636

v. In non-terminating fractions, the decimals do not end.

The given non-terminating fractions are converted to decimals. They are rounded off to 3 significant digits.

a) 1/3 = 0.333

b) 5/6 = 0.833

c) 2/7 = 0.285

d) 4/9 = 0.444

i. The number of significant digits in the given numbers is

a) 0.85 - 2 significant digits b) 22.4 - 3 significant digits

c) 0.849 - 3 significant digits d) 501.381 - 6 significant digits

e) 0.435 - 3 significant digits f) 1.233 - 4 significant digits

g) 0.71 - 2 significant digits h) 0.1473 - 4 significant digits

ii. Examples of terminating fractions are 1/3, 2/5, etc.

Examples of recurring fractions are 0.999..., 0.8333...., etc.

Examples of non-terminating fractions are 0.11...., 0.5454...

iii. The given numbers are rounded off up to 3, 4, and 5 significant figures.

a) 612737:

Up to 3 significant figures = 613000

Up to 4 significant figures = 612700

Up to 5 significant figures = 612740

c) 289.923:

Up to 3 significant figures = 290

Up to 4 significant figures = 289.9

Up to 5 significant figures = 289.92

e) 53.3728:

Up to 3 significant figures = 53.4

Up to 4 significant figures = 53.37

Up to 5 significant figures = 53.373

iv. The given terminating fractions are converted to decimals.

a) 1/4 = 0.250 b) 3/5 = 0.600 c) 2/9 = 0.222 d) 5/6 = 0.833

e) 7/8 = 0.875 f) 7/11 = 0.636

v. The given non-terminating fractions are converted to decimals.

a) 1/3 = 0.333 b) 5/6 = 0.833 c) 2/7 = 0.285 d) 4/9 = 0.444

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