Sem 2 GEOA 2020 Rounding off Angular Measurement

Sem 2 GEOA (2020) Rounding off & Angular Measurement Chandan Surabhi Das Barasat Govt. College

Definition: Rounding • Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. • Example: 7. 3 rounds to 7 Because 7. 3 is closer to 7 than to 8 • But what about 7. 5? Is it closer to 7 or closer to 8? It is half-way in between, so what should we do? Negative Numbers • -7. 4 rounds up to -7 • -7. 5 rounds down to -8 • -7. 6 rounds down to -8

Rounding to Tens, Tenths, Whatever. . . • Example: "Half Round Up" to tens (nearest 10): 25 rounds up to 30 24. 97 rounds down to 20 • Example • "Half Round Up" to hundredths (nearest 1/100): • 0. 5168 rounds up to 0. 52 • 1. 41119 rounds down to 1. 41

Rounding Decimals • Rounding to tenths means to leave one number after the decimal point. • Rounding to hundredths means to leave two numbers after the decimal point. EX: 3. 1416 rounded to hundredths is 3. 14, as the next digit (1) is less than 5 EX: 3. 1416 rounded to thousandths is 3. 142, as the next digit (6) is more than 5 EX: 1. 2735 rounded to 3 decimal places is 1. 274, as the next digit (5) is 5 or more

Rounding Whole Numbers • We may want to round to tens, hundreds, etc, In this case we replace the removed digits with zero. EX: 134. 9 rounded to tens is 130, as the next digit (4) is less than 5 EX: 12, 690 rounded to thousands is 13, 000, as the next digit (6) is 5 or more EX: 15. 239 rounded to ones is…………? EX: 16. 556 rounded to ones is…………? EX: 10. 999 rounded to ones is…………? EX: 105. 9 rounded to tens is…………. ? EX: Round 97, 870 to the nearest thousand……. . ?

Rounding to Significant Digits To round to "so many" significant digits, count digits from left to right, and then round off from there. EX: 1. 239 rounded to 3 significant digits is 1. 24, as the next digit (9) is 5 or more EX: 134. 9 rounded to 1 significant digit is 100, as the next digit (3) is less than 5 EX: 0. 0165 rounded to 2 significant digits is 0. 017, as the next digit (5) is 5 or more (0 is not a significant number)

For example 1, 654 to the nearest thousand is ………. . . To the nearest 100 it is ……………. To the nearest ten it is ……………. Express 0. 4563948 to three decimal places………………….

Measurement: Linear, Angular • The Linear Measurement includes measurements of length, diameters, heights and thickness The Angular measurement includes the measurement of angles. • Angle is a measurement that we can measure between the two line which meets at one point. Angular measurements are playing a very crucial role in measurements. • The most contemporary units are the degree ( ° ) and radian (rad) • SI unit of angular measure is the radian

• Angle Measurement – Degree Measure • A complete revolution, i. e. when the initial and terminal sides are in the same position after rotating clockwise or anticlockwise, is divided into 360 units called degrees. So, if the rotation from the initial side to the terminal side is (1360)th of a revolution, then the angle is said to have a measure of one degree. It is denoted as 1°. • We measure time in hours, minutes, and seconds, where 1 hour = 60 minutes and 1 minute = 60 seconds. Similarly, while measuring angles, • 1 degree = 60 minutes denoted as 1° = 60′ • 1 minute = 60 seconds denoted as 1′ = 60″

Angle Measurement – Radian Measure • Radian measure is slightly more complex than the degree measure. Imagine a circle with a radius of 1 unit. Next, imagine an arc of the circle having a length of 1 unit. The angle subtended by this arc at the centre of the circle has a measure of 1 radian. Here is how it looks:

: Radian Measure • n a circle of radius r, an arc of length r subtends an angle of 1 radian at the centre. Hence, in a circle of radius r, an arc of length l will subtend an angle = ( frac {l}{r} ) radian. Generalizing this, we have, in a circle of radius r, if an arc of length l subtends an angle θ radian at the centre, then • θ = lr : • Radian measure = π180° x Degree measure = 180°π x Radian measure

Example 1 • Convert 40° 20′ into radian measure.