เฉลย แบบฝึกหัด 3.3 ก ข้อ 2

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แบบฝึกหัด 3.3 ก (ข้อ 3) [ม.1 เล่ม 1 บทที่ 3 เลขยกกำลัง : สสวท. 2560]

3. จงหาค่าของจำนวนที่อยู่ในรูปสัญกรณ์วิทยาศาสตร์ต่อไปนี้

1) 4 x \(\mathtt{10^5}\)

วิธีทำ

4 x \(\mathtt{10^5}\)

= 4 x 100,000

ตอบ 400,000

 

2) 3.8 x \(\mathtt{10^6}\)

วิธีทำ

3.8 x \(\mathtt{10^6}\)

= 3.8 x 1,000,000

ตอบ 3,800,000

 

3) 1.45 x \(\mathtt{10^9}\)

วิธีทำ

1.45 x \(\mathtt{10^9}\)

= 1.45 x 1,000,000,000

ตอบ 1,450,000,000

 

4) 8.257 x \(\mathtt{10^4}\)

วิธีทำ

8.257 x \(\mathtt{10^4}\)

= 8.257 x 10,000

ตอบ 82,570

 

5) 5.006 x \(\mathtt{10^{10}}\)

วิธีทำ

5.006 x \(\mathtt{10^{10}}\)

= 5.006 x 10,000,000,000

ตอบ 50,060,000,000

 

6) 6.0526 x \(\mathtt{10^{12}}\)

วิธีทำ

6.0526 x \(\mathtt{10^{12}}\)

= 6.0526 x 1,000,000,000,000

ตอบ 6,052,600,000,000

1. จงเขียนจำนวนในแต่ละข้อต่อไปนี้ในรูปสัญกรณ์วิทยาศาสตร์

1) 70,000

ตอบ 7 x \(\mathtt{10^4}\)

= (2.1 x 10) x \(\mathtt{10^4}\)
 = 2.1 x (10 x \(\mathtt{10^4}\))
 = 2.1 x \(\mathtt{10^{1 \, + \, 4}}\)
 = 2.1 x \(\mathtt{10^5}\)

ตอบ 2.1 x \(\mathtt{10^5}\)

= (4.06 x 100) x \(\mathtt{10^4}\)
 = (4.06 x \(\mathtt{10^2}\)) x \(\mathtt{10^4}\)
 = 4.06 x (\(\mathtt{10^2}\) x \(\mathtt{10^4}\))
 = 4.06 x \(\mathtt{10^{2 \, + \, 4}}\)
 = 4.06 x \(\mathtt{10^6}\)

ตอบ 4.06 x \(\mathtt{10^6}\)

วิธีทำ

56,700,000

= 567 x 100,000

= (5.67 x 100) x \(\mathtt{10^5}\)
 = (5.67 x \(\mathtt{10^2}\)) x \(\mathtt{10^5}\)
 = 5.67 x (\(\mathtt{10^2}\) x \(\mathtt{10^5}\))
 = 5.67 x \(\mathtt{10^{2 \, + \, 5}}\)
 = 5.67 x \(\mathtt{10^7}\)

ตอบ 5.67 x \(\mathtt{10^7}\)

วิธีทำ

15,006,000

= 15,006 x 1,000

= (1.5006 x 10,000) x \(\mathtt{10^3}\)
 = (1.5006 x \(\mathtt{10^4}\)) x \(\mathtt{10^3}\)
 = 1.5006 x (\(\mathtt{10^4}\) x \(\mathtt{10^3}\))
 = 1.5006 x \(\mathtt{10^{4 \, + \, 3}}\)
 = 1.5006 x \(\mathtt{10^7}\)

ตอบ 1.5006 x \(\mathtt{10^7}\)

วิธีทำ

8,000,000,000

= 8 x 1,000,000,000

ตอบ 8 x \(\mathtt{10^9}\)

วิธีทำ

490,000,000,000

= 49 x 10,000,000,000

= (4.9 x 10) x \(\mathtt{10^{10}}\)
 = 4.9 x (10 x \(\mathtt{10^{10}}\))
 = 4.9 x \(\mathtt{10^{1 \, + \, 10}}\)
 = 4.9 x \(\mathtt{10^{11}}\)

ตอบ 4.9 x \(\mathtt{10^{11}}\)

วิธีทำ

70,101,000,000

= 70,101 x 1,000,000

= (7.0101 x 10,000) x \(\mathtt{10^6}\)
 = (7.0101 x \(\mathtt{10^4}\)) x \(\mathtt{10^6}\)
 = 7.0101 x (\(\mathtt{10^4}\) x \(\mathtt{10^6}\))
 = 7.0101 x \(\mathtt{10^{4 \, + \, 6}}\)
 = 7.0101 x \(\mathtt{10^{10}}\)

ตอบ 7.0101 x \(\mathtt{10^{10}}\)

วิธีทำ

24,500,000,000,000

= 245 x 100,000,000,000

= (2.45 x 100) x \(\mathtt{10^{11}}\)
 = (2.45 x \(\mathtt{10^2}\)) x \(\mathtt{10^{11}}\)
 = 2.45 x (\(\mathtt{10^2}\) x \(\mathtt{10^{11}}\))
 = 2.45 x \(\mathtt{10^{2 \, + \, 11}}\)
 = 2.45 x \(\mathtt{10^{13}}\)

ตอบ 2.45 x \(\mathtt{10^{13}}\)

วิธีทำ

19,567,000,000,000

= 19,567 x 1,000,000,000

= (1.9567 x 10,000) x \(\mathtt{10^9}\)
 = (1.9567 x \(\mathtt{10^4}\)) x \(\mathtt{10^9}\)
 = 1.9567 x (\(\mathtt{10^4}\) x \(\mathtt{10^9}\))
 = 1.9567 x \(\mathtt{10^{4 \, + \, 9}}\)
 = 1.9567 x \(\mathtt{10^{13}}\)

ตอบ 1.9567 x \(\mathtt{10^{13}}\)